Analytical noncovalent electrochemistry for battery engineering

Noncovalent bonding interactions are ubiquitous in the natural world, exerting a pivotal influence on the maintenance of dynamic supramolecular and biological functions within DNA^1,2, proteins³ and various other biomacromolecules⁴. These interactions have bestowed on us the capability to fabricate artificial molecular machines^5,6,7,8, consequently granting us fine control over the properties of materials at the molecular level. Moreover, they constitute an additional manifestation of chemical bonding, potentially introducing a fresh dimension of regulation into the realm of chemical engineering. In an attempt to unravel and scrutinize these noncovalent interactions, a multitude of characterization methodologies that are primarily dependent on spectroscopic techniques have been utilized. Among these techniques, ultraviolet–visible⁹ (UV–vis) and fluorescence emission spectroscopies¹⁰ are prominent, collectively constituting the established bedrock of noncovalent spectroscopies. Nevertheless, the applicability of noncovalent spectroscopies is somewhat constricted as these characterization methods hinge on specific superstructures to elicit spectroscopic responses. It is thus imperative to establish alternative tools for the characterization of noncovalent bonding interactions, as well as to introduce methodologies that extend the repertoire beyond the current paradigms.

In addition to these conventional spectroscopic techniques, electrochemical signals obtained via cyclic voltammetry (CV) and differential pulse voltammetry (DPV) have also been integrated¹¹ into the exploration of noncovalent bonding interactions. For instance, researchers have used the comparative analysis of redox peaks from complexes and their corresponding host/guest components^12,13. This approach enables the identification of newly formed supramolecular entities, consequently implying the presence of noncovalent bonding interactions. Within this framework, however, the intricate connection between noncovalent interactions and electrochemistry remains largely unclarified, along with the underlying mechanisms and establishing titration methods in the case of analytical electrochemistry. For example, the strength of noncovalent interactions, quantified through binding constants (K_a) within host–guest complexes, has pivotal implications for both foundational investigations and practical applications^14,15,16. The assessment of the strength of noncovalent interactions, however, has become dependent heavily on spectroscopic methods, whose signals possess a roughly linear relationship¹⁷ (for example, the Lambert–Beer law) with respect to the concentration of the host or guest or their complex, despite the fact that the accuracy^18,19 of these approaches has been less than satisfactory. Electrochemistry provides another perspective from which to study noncovalent interactions. Under the control of physicochemical laws, the thermodynamic potential is strictly and accurately related to the change in the Gibbs free energy (ΔG) caused by noncovalent interactions. Nevertheless, the quantification (such as through K_a values) of noncovalent interactions on the basis of electrochemical principles remains an area of relatively limited exploration. In essence, the interplay between noncovalent bonding interactions and electrochemistry, from the standpoint of analytical chemistry, is an emerging discipline (Fig. 1a) which has yet to be fully established.

a, Schematic of different analytical methods for investigating noncovalent interactions featuring the proposed electrochemical strategy (left) and traditional spectroscopic characterization (right). The electrochemical signals are associated directly with various physicochemical properties and potentially minimize experimental errors during the evaluation of noncovalent interactions. b, The redox reactions summarized by C⁴⁺/C^2(•+)/C⁰ (left) and the complexation between C⁴⁺ and En to form En⊂C⁴⁺ host–guest complexes (right). From the perspective of the Nernst equation (in the dashed box), the addition of En consumes C⁴⁺ and reduces the equilibrium potential (φ₁) for the C⁴⁺/C^2(•+) redox couple. e⁻, electron; φ₁^⦵, standard potential; R, gas constant; T, absolute temperature; z, electron transfer number; F, Faraday constant. c, CV (top) and DPV (bottom) curves of 1.0 mM C⁴⁺ before (blue line) and after (red line) the addition of 2.0 mM E6. The electrochemical characterization was performed in acetonitrile (MeCN) with 0.1 M tetrabutylammonium hexafluorophosphate (TBAPF₆) as the supporting electrolyte and Ag/AgCl as the reference electrode. The peaks of C⁴⁺/C^2(•+) shift to a lower potential, an observation that is consistent with the above theoretical analysis. By contrast, the peaks of C^2(•+)/C⁰ are not affected by the negligible interactions between En and C^2(•+)/C⁰.

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If the quantitative relationship between noncovalent interactions and electrochemistry can be established from the standpoint of analytical chemistry, it could provide a new dimension for the precise control of electrochemical properties. For instance, in battery systems, the electrochemical properties of each component, including the electrodes, electrolytes and additives/catalysts, must be located precisely within narrow ranges to demonstrate the best battery performance. For instance, the redox potential of the redox mediator in oxygen- or sulfur-based cathodes must fall within a very narrow potential range to ensure that the catalytic process is thermodynamically feasible and kinetically favorable^20,21. Therefore, if analytical noncovalent electrochemistry can be established, one should be able to modulate the electrochemical performance of battery systems by introducing and controlling the noncovalent interactions. Hence, it is an opportune time to introduce a systematic methodology for carrying out noncovalent electrochemical analysis and facilitating the development of application-oriented electrochemical engineering.

Electrochemical responses to noncovalent interactions

We have selected a host–guest system to demonstrate the noncovalent electrochemical method of analysis. The host, cyclobis(paraquat-p-phenylene)^22,23 (C⁴⁺), is a tetracationic cyclophane that contains two separate bipyridinium (BIPY²⁺) units that are electrochemically active. C⁴⁺ (Fig. 1b, left) has two reduction potentials associated with its radical cationic (C^2(•+)) and neutral (C⁰) states²⁴, corresponding to the equilibrium potential (φ) values for the C⁴⁺/C^2(•+) and C^2(•+)/C⁰ redox couples associated with φ₁ and φ₂, respectively. The thread-like guest consists of a naphthalene unit with appended –(OCH₂CH₂)_nOH groups at its 1 and 5 positions, that is, En, where n refers to the number of repeating units present in the oligoethylene glycol chains. The donor–acceptor interactions between the BIPY²⁺ units in C⁴⁺ and the 1,5-dioxynaphthalene units in En are typical noncovalent interactions²⁵, which drive (Fig. 1b upper and Supplementary Figs. 4–8) the formation of the inclusion complexes (En⊂C⁴⁺). The C^2(•+) and C⁰ states are relatively electron-rich and exhibit negligible interactions²⁶ with the En guests.

To establish a sound theoretical foundation for analytical noncovalent electrochemistry, we investigated the impact of noncovalent interactions on the electrochemical measurements. Upon the addition of En to the redox system of C⁴⁺/C^2(•+), En combines selectively with C⁴⁺ to form host–guest complexes. As a result, the chemical potential (μ) of the oxidized species decreases, leading to a negative shift in the equilibrium potential (φ). Furthermore, the shifts in the equilibrium potential values can be rationalized by relating them to the concentrations of the redox components. With all the components in balance, we can determine the equilibrium potential using any of the redox couples in accordance with the Nernst equation. We have selected the C⁴⁺/C^2(•+) redox system for investigation. Specifically, En consumes free C⁴⁺ and the concentration of free C⁴⁺ ([C⁴⁺]) is reduced. According to the Nernst equation, the reduced [C⁴⁺] leads to a reduction of the equilibrium potential from φ₁ to φ₁′. This analysis was confirmed by the CV and DPV curves in which the peaks for the C⁴⁺/C^2(•+) redox system undergo a negative shift following the addition of En (Fig. 1c and Supplementary Fig. 11). Conversely, the peaks corresponding to the redox couple C^2(•+)/C⁰ remain unaffected since there are only weak interactions between En and C^2(•+) or C⁰. The combination of theoretical and experimental results leads to the conclusion that electrochemical signals are able to serve as probes for detecting noncovalent interactions.

Measuring K _a values using electrochemical titrations

Using the Nernst relationship, the shift in equilibrium potential (Δφ = φ₁ − φ₁′, defined as the difference in equilibrium potential before and after the addition of En) can be expressed quantitatively as a function of the binding constant (K_a) and the guest/host ratio (x = [En]₀/[C]₀, defined as the En molar equivalent relative to C⁴⁺). According to the stoichiometry of the complexation, the concentrations of free C⁴⁺ and En⊂C⁴⁺ ([C⁴⁺] and [En⊂C⁴⁺], respectively) can be determined from the K_a values and [En]₀/[C]₀ (Fig. 2a). Furthermore, Δφ can be calculated using the Nernst equation. The plot of Δφ versus [En]₀/[C]₀ (Fig. 2b) is typically sigmoidal in shape with a sudden jump in the titration at the equivalence point when [En]₀/[C]₀ = 1. The reason for the jump is that Δφ exhibits a logarithmic relationship with respect to [C⁴⁺], which undergoes a rapid change in its order of magnitude around the equivalence point. For systems with different K_a values (Fig. 2b), the titration curves in the range of 0 < [En]₀/[C]₀ < 1 are similar, whereas they become distinct when [En]₀/[C]₀ > 1. The potential shift Δφ has a positive correlation with the K_a value, especially in the case of the titration curve where the titration equivalent is greater than 1. By acquiring and fitting the titration curve, one can measure the K_a values of the host–guest complexes rather easily. The titrations were performed using an electrochemical cell (Fig. 2c and Supplementary Figs. 14–18) utilizing a micro-syringe to inject a specific amount of the En feedstock solution into 1 mM C⁴⁺. With the increase in En equivalents during the titration, the redox potential of C⁴⁺/C^2(•+) showed a gradual negative shift whereas the redox potential of C^2(•+)/C⁰ remained unchanged (Fig. 2d and Supplementary Figs. 19 and 20). The potential shift Δφ in the redox potential of C⁴⁺/C^2(•+) at different titration steps was measured on the basis of the peak position changes in the DPV curves. By fitting the titration results, the K_a values of En⊂C⁴⁺ (n = 0, 2, 3, 6) were measured and found to be 1.9 × 10³, 1.9 × 10⁴, 5.0 × 10⁴ and 1.2 × 10⁵ M⁻¹, respectively (Fig. 2e and Supplementary Fig. 21). These binding constants are correlated positively with the lengths of the oligoethylene glycol chains in En, as a result of the enhanced [C–H···O] interactions²⁷ between C⁴⁺ and the oligoethylene glycol chains in En. These results, which are consistent with previously reported data²⁸, demonstrate the effectiveness of electrochemical titrations.

a, Titration of C⁴⁺ using En, showing the numerical simulation of the concentration of C⁴⁺ ([C⁴⁺], blue line) and En⊂C⁴⁺ ([En⊂C⁴⁺], green line) with different K_a values, for K_a = 10³ M⁻¹ (solid line) and K_a = 10⁴ M⁻¹ (dashed line). The initial concentration of C⁴⁺ ([C]₀) is set to [C]₀ = 1 mM. c, [C⁴⁺] or [En⊂C⁴⁺]. b, Numerical simulation of the potential shift (Δφ) of C⁴⁺/C^2(•+) at different En equivalents ([En]₀/[C]₀) and K_a values. The Δφ–[En]₀/[C]₀ curve is typically sigmoidal in shape with a titration jump at the equivalence point. Different K_a values correspond to distinct Δφ–[En]₀/[C]₀ curves, especially to the right of the equivalence point. c, Schematic of the setup used in the electrochemical titration by adding En to C⁴⁺. WE, working electrode; CE, counter electrode; RE reference electrode. d, DPV curves at each En equivalent during the addition of 1.0 mM C⁴⁺ to E6, where Δφ at each En equivalent was recorded. e, Measured Δφ at different En equivalents during the electrochemical titration of C⁴⁺ with E0 (light red) or E6 (deep red), together with the fitting results (dashed lines) and the measured K_a values for E0⊂C⁴⁺ and E6⊂C⁴⁺. The anomalies in the theoretical and experimental electrochemical titration curves for titration with E6 imply the existence of 2:1 host–guest complexes.

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On the basis of the 1:1 binding model for the host–guest complex, the curve fitting of the E0⊂C⁴⁺ titration agrees well with the experimental data. For the En⊂C⁴⁺ titrations (n = 2, 3, 6), however, the curve fitting (Fig. 2e and Supplementary Fig. 21a), is not in good agreement with the experimental data in the interval of 0 < [En]₀/[C]₀ < 1. Specifically, the recorded Δφ in the range of 0 < [En]₀/[C]₀ < 1 is higher than the theoretical maximum value of Δφ corresponding to a K_a value of infinity. This result implies that the consumption of C⁴⁺ is greater than the theoretical maximum based on the 1:1 binding model. A possibility is that each En guest interacts with more than one C⁴⁺ host, forming a 2:1 host–guest complex, that is, a [3]pseudorotaxane (En⊂2C⁴⁺). Accordingly, we investigated a 2:1 host–guest model, where the first and second stepwise association constants are K_a1 and K_a2, respectively (Fig. 3a). The overall association constant for the 2:1 host–guest complex is β₂₁ (β₂₁ = K_a1 × K_a2). The curve fitting (Fig. 3b) matches well with the experimental data across the full range of En equivalents, and the values of K_a1, β₂₁ and K_a2 can be acquired. On the basis of the K_a1 and K_a2 values, the interaction parameter (α) for each En⊂2C⁴⁺ is calculated to be lower than 1, indicating that these systems display negative cooperativity. The concentrations of free C⁴⁺ and the En⊂C⁴⁺ and En⊂2C⁴⁺ complexes at different equivalents can also be calculated (Fig. 3c and Supplementary Fig. 27). The formation of En⊂2C⁴⁺ is dominant when the equivalence is lower than 1. When the En equivalence increases, the formation of the En⊂C⁴⁺ is more favorable.

a, Graphical representation of the proposed hypothesis, where a 2:1 host–guest complex (En⊂2C⁴⁺) is formed during the initial titration stage. During this initial titration stage, C⁴⁺ is in excess with respect to En, a situation that is favorable for the formation of En⊂2C⁴⁺. When more equivalents of En are added, En⊂2C⁴⁺ transforms into the En⊂C⁴⁺ 1:1 host–guest complex. b, Measured Δφ at different En equivalents during electrochemical titration, together with the fitting results (solid lines) based on the model presented in a, where the formation of both En⊂C⁴⁺ and En⊂2C⁴⁺ host–guest complexes are taken into consideration. The dashed lines are the fitting results based on 1:1 binding model. c, Numerical simulation of the concentrations of C⁴⁺, E6⊂C⁴⁺ and E6⊂2C⁴⁺ (with structures shown schematically as insets) at different equivalents of E6. The results show that the formation of En⊂2C⁴⁺ is favoured in the case of an excess of C⁴⁺, inspiring us to search for evidence of the existence of En⊂2C⁴⁺ under the conditions where C⁴⁺ is in excess. d, Single-crystal superstructure of the En⊂2C⁴⁺ host–guest complex. The host–guest ratio was determined to be 2:1. MeCN solvent molecules and PF₆⁻ counterions are omitted for clarity. e, Electrospray ionization mass spectra of the solution containing 1.0 mM C⁴⁺ and 0.2 mM E6, where the co-existence of C⁴⁺, E6⊂C⁴⁺ and E6⊂2C⁴⁺ (shown as insets) can be observed. f, Evolution of the UV–vis spectra with the addition of E6 to 1 mM C⁴⁺ solution. The red-shift tendency (dashed line) indicates that the dominant species changes from E6⊂2C⁴⁺ (left inset) to E6⊂C⁴⁺ (right right) with the addition of E6.

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Uncovering a 2:1 host–guest complex

On the basis of the results of the electrochemical titrations, we predicted that a 2:1 host–guest complex between C⁴⁺ and En can be formed. To confirm this prediction, single crystals were obtained by evaporating ⁱPr₂O into a solution of C⁴⁺ and En in MeCN with C⁴⁺ present in excess. Single-crystal X-ray diffraction analysis (Fig. 3d and Extended Data Fig. 1) demonstrated the formation of the 2:1 host–guest complex En⊂2C⁴⁺ in which one En guest is embraced by two C⁴⁺ host rings. We also observed the formation of En⊂2C⁴⁺ in the solution state, as shown using high-resolution electrospray ionization mass spectrometry (Fig. 3e). In a solution containing a mixture of C⁴⁺ and E6, the mass spectrum exhibited prominent peaks at mass-to-charge ratio (m/z) values of 405.0948, 749.2787 and 1,299.8397, in agreement with the calculated m/z values for [C·2PF₆]²⁺, [E6⊂C·2PF₆]²⁺ and [E6⊂2C·6PF₆]²⁺, respectively. The formation of E2⊂2C⁴⁺ and E3⊂2C⁴⁺ was also confirmed (Supplementary Fig. 31) by mass spectrometry. The formation of these 2:1 host–guest complexes was also indicated using UV–vis spectroscopy (Fig. 3f). At a low En equivalents, the charge-transfer absorption bands were located at ~480 nm. When the En equivalents was increased, a new absorption band located at ~520 nm emerged and became dominant. According to time-dependent density functional theory calculations, the bands located at approximately 480 and 520 nm can be assigned to the 2:1 and 1:1 host–guest complexes, respectively (Supplementary Fig. 35). The redshift in the wavelength (λ) arises from the fact that the proportion of the 1:1 complex gradually dominates that of the 2:1 complex with the increase in En equivalents. Furthermore, on the basis of the binding model associated with 1:1 and 2:1 host–guest equilibria, the UV–vis titration curves give a better fit when based on the binding model of the 1:1 host–guest equilibrium (Supplementary Fig. 34). These experimental results confirm our prediction of the formation of the 2:1 complex, demonstrating that the electrochemical analysis can, in some cases, provide more detailed information than traditional spectroscopic analysis because of the high sensitivity of the electrochemical signal with respect to the concentration. The traditional spectroscopic signals are correlated linearly with the absolute concentration, for example, the concentration of En⊂C⁴⁺ for the UV–vis spectra. By contrast, the electrochemical potential signal and the concentration are related logarithmically. Even a very small difference in concentration can therefore result in a large change in the potential.

Advantages of the noncovalent electrochemical method of analysis

The higher sensitivity of the electrochemical signal towards the concentration enables the accurate measurement of noncovalent interactions for systems with high K_a values. Compare (Fig. 4a,b and Extended Data Fig. 2) UV–vis spectroscopic and electrochemical analyses in relation to their sensitivity to variations in K_a values. Setting [C]₀ to be 1 mmol L⁻¹, the UV–vis spectroscopic absorptions are sensitive to K_a values in the range of 10²–10⁴ M⁻¹. In contrast, electrochemical signals are more sensitive to the systems with high K_a values, particularly for those values greater than 10³ M⁻¹. For example, with [C]₀ set to be 1 mmol L⁻¹, the two theoretical UV–vis titration curves (K_a = 10⁵ and 10⁶ M⁻¹) reproduced in Fig. 4c are nearly identical, while the two theoretical electrochemical titration curves (K_a = 10⁵ and 10⁶ M⁻¹) are clearly distinguishable. In the case of UV–vis titrations during K_a measurements, although their accuracy can be improved theoretically by reducing [C]₀, the relative error of absorbance also increases considering the relatively low molar extinction coefficient of this host–guest system. Thus, for several host–guest systems (with low molar extinction coefficients and high K_a values), electrochemical methods can provide more reliable K_a values.

a, Spectroscopic Abs/Abs_sat signals and electrochemical Δφ signals at different K_a values, where Abs and Abs_sat denote the absorbance and saturation absorbance, respectively. Abs/Abs_sat and Δφ are collected at the En equivalents of 1.0 and 5.0, respectively. A higher tangential slope corresponds to a higher sensitivity in the variation of the K_a values. K_a0 is the intercept of the asymptote of the red curve at the x axis. b, The differential curves of the data in a. A higher numerical value corresponds to a higher measurement accuracy. The electrochemical titration is more accurate when investigating host–guest complexes with larger K_a values. c, Numerical simulation of the UV–vis titration curves (dashed lines; left axis) and the electrochemical titration curves (solid lines; right axis) under different K_a values, for K_a = 1 × 10⁵ M⁻¹ (light blue lines) and K_a = 1 × 10⁶ M⁻¹ (dark blue lines). The open red circles are the UV–vis titration results (left axis); the filled red circles are the electrochemical titration results (right axis). Both titrations were carried out by adding E6 to 1 mM C⁴⁺ solution. It is clear that the electrochemical titration is more accurate when measuring the K_a value of the E6⊂C⁴⁺ complex. d, The CV features of the host–guest complexes are determined via multiple properties, including K_a, D, p and Δφ_βα^⊖, which can be obtained through data digging. ΔE_p, change in peak potential; i_pa, anodic peak current; i_p, peak current; A, area of the WE; v, scan rate. e, Characteristic results of multiple properties of the host C⁴⁺ and its host–guest complexes acquired via electrochemical analysis.

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Besides measuring binding constants (K_a values), electrochemical analysis can provide additional information, including the diffusion coefficient (D), the guest/host stoichiometric ratio (p) and the equilibrium potential gap of two single-electron transfer processes (Δφ_βα^⊖ = φ_β^⊖ − φ_α^⊖), which are embodied, respectively, in the peak heights²⁹, positions³⁰ and shapes³¹ of the CV curves (Fig. 4d). Among them, Δφ_βα^⊖ is the equilibrium potential gap between single-electron transfer processes α (C⁴⁺ + e⁻ = C^2+(•+)) and β (C^2+(•+) + e⁻ = C^2(•+)). Electrochemical curves offer a wealth of information pertaining to complexes. By processing and analysing electrochemical data, multiple properties of complexes can be obtained. For instance, the application of linear regression to the peak current resulting from the electrochemical reduction in relation to the CV scan rates enables the determination of D for the complexes. Notably, as the length of the oligoethylene glycol chains in En is extended, the initial augmentation of D rises from the elevated complex–solvent affinity, in going from E0 to E2. Subsequently, in going from E2 to E6, a decline in D is observed because of the increase in molecular weight. Furthermore, using curve-fitting techniques for the electrochemical titration curve, the stoichiometric ratio of the guest–host interaction can be extracted. This approach is particularly noteworthy as it demonstrates the feasibility of investigating thoroughly even the most unfamiliar supramolecular systems, achieved as a result of the sequential analysis of stoichiometric ratios and binding constants.

The detailed principles for the measurement of noncovalent interactions can be found in Supplementary Information (Supplementary Figs. 38–42), and result in the data presented in Fig. 4e. In short, the noncovalent electrochemical method of analysis can measure several physicochemical properties of complexes. Furthermore, the proposed electrochemical analyses demonstrate (Supplementary Figs. 43–46) excellent universality when investigating host–guest complexes possessing host/guest ratios with different noncovalent interactions in a range of solvents. As a result, the noncovalent electrochemical analytical methodology is an important complement to the current spectroscopic methods. Electrochemical analyses enrich the toolbox of comprehensive and accurate measurements in supramolecular chemistry.

Analytical noncovalent electrochemistry in batteries

Analytical noncovalent electrochemistry bridges the gap between fundamental supramolecular chemistry and its application in electrochemical engineering. In contrast to other material categories, supramolecular complexes are uniquely defined by discernible noncovalent interactions, which can be regulated meticulously via host–guest interactions to reveal the properties of the complexes. These distinctive attributes also underpin their promising potential within the realm of energy chemistry and engineering. The application of supramolecular complexes in energy electrochemical engineering, however, is still relatively limited, largely because of an insufficient understanding of the relationship between noncovalent interactions and electrochemical behavior, as well as the inability to measure these supramolecular properties accurately. Fortunately, with the advent of analytical noncovalent electrochemistry, one can design and screen host–guest complexes towards the target of electrochemical engineering. To demonstrate this application, we explored the feasibility of using noncovalent regulation utilizing complexes as homogeneous catalysts in lithium–sulfur batteries.

Lithium–sulfur batteries are amongst the next generation of energy-storage devices^32,33 as a consequence of their ultrahigh theoretical energy density (2,600 Wh kg⁻¹), which is around ten times larger than that of their current lithium-ion counterparts. The redox behavior of sulfur species in cathodes, however, is sluggish when it comes to kinetics³⁴, restricting the battery performance. Homogeneous catalysts (also commonly referred to as redox mediators) in lithium–sulfur batteries undergo reversible redox reactions to set up chemical–electrochemically coupled circular reactions as the bypass and thus catalyse the charging/discharging processes^35,36. In the search for a good homogeneous catalyst for sulfur redox, three criteria must be met. (1) Viable thermodynamics: when catalysing the discharging process, the equilibrium potential of the catalyst should be slightly lower than that of the sulfur species (φ_S, the equilibrium potential of the polysulfide redox reaction) to ensure the occurrence of the chemical reaction while minimizing the overpotential³⁷. The opposite is true for the charging process³⁸. (2) Favorable kinetics: fast redox kinetics associated with the catalyst ensure favorable catalytic cycles³⁹. (3) Efficient diffusion: the catalyst should be efficient when it comes to shuttling between the electrode surfaces and bulk-phase electrolytes⁴⁰ to activate the inert sulfur species. The screening/design of homogeneous catalysts in lithium–sulfur batteries presents a multitude of stringent demands. A single species other than a supramolecular complex makes it challenging to fulfill all of these requirements. By contrast, supramolecular complexes introduce another dimension of noncovalent interactions, holding the promise of addressing the aforementioned requirements precisely and thereby enabling the selection of optimal homogeneous catalysts.

The host C⁴⁺ encompasses two distinct redox processes involving C⁴⁺/C^2(•+) and C^2(•+)/C⁰ transitions. These two redox couples ensure the catalytic capability of C⁴⁺ for both polysulfide oxidation (which requires C⁴⁺/C^2(•+)) and polysulfide reduction (which requires C^2(•+)/C⁰). Whereas the latter redox transformation (C^2(•+)/C⁰, φ₂) aligns with the criterion of viable thermodynamics that are suitable for catalysing the polysulfide reduction, the former redox transition (C⁴⁺/C^2(•+), φ₁) falls short of the viable thermodynamics criterion because of its significantly elevated equilibrium potential in comparison with φ_S. Our inspiration stems from the principles of analytical noncovalent electrochemistry, which advocate the introduction of noncovalent interactions to tailor redox potentials. By engaging species that are capable of interacting selectively with C⁴⁺ through appropriate K_a values, it becomes possible to reduce the equilibrium potential of C⁴⁺/C^2(•+) with precision to achieve a desired value (slightly exceeding φ_S). To this end, our approach involves the utilization of E6, a guest that exhibits pronounced noncovalent interactions with C⁴⁺, forming an E6⊂C⁴⁺ complex, while exhibiting minimal interactions with C^2(•+) or C⁰. During noncovalent modulation, φ₁ is effectively tuned to a suitable value of φ₁′ (marginally higher than φ_S), while φ₂ is cautiously maintained slightly below φ_S (Fig. 5a). In this context, E6 functions as a co-catalyst (Extended Data Fig. 3) that effectively modulates the properties of C⁴⁺. The E6⊂C⁴⁺ complex thus formed serves as a pivotal catalyst in operational lithium–sulfur batteries. Furthermore, the evaluation of the reaction rate constant (k₀) and diffusion coefficient (D) reveals that E6⊂C⁴⁺ outperforms sulfur entities by a factor of 7.5 and 5.3, respectively (Fig. 5a inset and Supplementary Figs. 50–52).

a, Three designing/screening criteria of homogeneous catalysts for sulfur redox reactions, namely viable thermodynamics, favorable kinetics and efficient diffusion. The i–φ diagram shows the volt–ampere curves for sulfur redox (orange line), a competent homogeneous catalyst (solid red line), and C⁴⁺/C^2(•+) without the addition of En (dashed red line). Specifically, the addition of E6 reduces the redox potential of C⁴⁺/C^2(•+) (from the dashed red line into the solid red line) to satisfy the first designing/screening criterion, making E6⊂C⁴⁺ a competent homogeneous catalyst. The insets show the k₀ (left) and D (right) data for Li₂S₆ and E6⊂C⁴⁺, indicating the satisfaction of the second and third designing/screening criteria. b, CV curves of E6⊂C⁴⁺ (catalytic amount, 1 mM), Li₂S₆ (10 mM) and their mixture (10 mM Li₂S₆ + 1 mM E6⊂C⁴⁺). The higher current responses for the sulfur species redox reactions with the addition of E6⊂C⁴⁺ demonstrate the remarkable catalytic activity of E6⊂C⁴⁺. c, Schematic of the catalytic mechanism of E6⊂C⁴⁺ for the sulfur redox reaction, including charging (upper cyclic reaction path) and discharging (lower cyclic reaction path) processes. d,e, Photograph (d) and galvanostatic discharge/charging profiles obtained at the initial discharging/charging process (e) of the lithium–sulfur pouch cell using E6⊂C⁴⁺ as a homogeneous catalyst. f, Comparison of the energy density of the rechargeable lithium–sulfur pouch cell in this work (cyan) and values reported in the literature (orange).

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Unsurprisingly, because it meets all of the screening criteria of viable thermodynamics, favorable kinetics and efficient diffusion, E6⊂C⁴⁺ does exert a striking bifunctional catalytic effect on the reduction and oxidation of sulfur species, represented by the strengthened CV current responses (Fig. 5b and Supplementary Figs. 53–57). In the case of the discharging process, the redox couple C^2(•+)/C⁰ sets up a reduction cyclic bypass (Fig. 5c), facilitating reduction of the sulfur species. For the charging process, E6 serves as a co-catalyst and modulates the electrochemical properties of the C⁴⁺/C^2(•+) couple (Fig. 5c and Extended Data Fig. 3). They work together to set up an oxidation cyclic bypass and strengthen the oxidation of polysulfide. The catalytic effect was also confirmed in working lithium–sulfur batteries. The specific capacities are improved by 237% (2.0C) and 24.6% (0.5C) with E6⊂C⁴⁺ as the catalyst in coin cells following routine and high sulfur loading, respectively (Supplementary Fig. 58). The catalytic effect is also long-lasting and provides a stable capacity enhancement in long-term cycling (Supplementary Fig. 60). More impressively, using the E6⊂C⁴⁺ catalyst, a 5.34 Ah lithium–sulfur pouch cell (Fig. 5d) delivers a high energy density of 495 Wh kg⁻¹ (Fig. 5e), an enhancement in comparison with previously documented^41,42,43 rechargeable lithium–sulfur pouch cells (Fig. 5f). In summary, noncovalent electrochemistry effectively serves as a bridge between noncovalent chemistry and electrochemistry. Electrochemistry affords a new perspective for measuring precisely the properties of noncovalent interactions. Conversely, the management of noncovalent interactions has emerged as a pivotal regulating dimension, bolstering the realm of energy electrochemical engineering. The exceptional catalytic prowess and the impressive battery performance demonstrated in this sector underscore the efficacy of analytical noncovalent electrochemistry in real-world applications. This achievement stands as a testament to the potency of noncovalent electrochemical approaches in addressing practical challenges.

The noncovalent electrochemical method of analysis, which constitutes a characterization tool for noncovalent interactions, possesses several advantages. (1) Universality: compared with spectroscopic analyses that rely on specific chemical probes to show spectroscopic responses, most of the groups that participate in noncovalent interactions are electrochemically active as long as the potential range is broad enough. Electrochemical analyses can be expanded to cover more types of noncovalent interaction. (2) Accuracy: the logarithmic relations ensure a better accuracy for K_a measurements when evaluating noncovalent systems with large K_a values. (3) Efficiency: noncovalent electrochemical analysis is a method that enables a thorough investigation of host–guest chemistry, which holds promise for practical applications. It should be noted that the noncovalent electrochemical method of analysis is not a panacea since detailed structural information cannot be deduced directly. By combining different characterization techniques and even developing electrochemistry–spectroscopy devices, comprehensive structural and physicochemical properties can be obtained to deepen our insights into sophisticated noncovalent interactions in the near future.

In conclusion, we propose an electrochemical method of analysis for investigating noncovalent interactions. Compared with traditional characterization methods, electrochemistry breaks through the limitations of structure-reliance and concentration-linear correlations, leading to irreplaceable advantages in universality, accuracy and efficiency. Using this strategy, a 2:1 host–guest complex was discovered, K_a values and other diversified properties of various complexes were measured and a high-performance supramolecular homogeneous catalyst was screened to achieve a breakthrough in the energy density of batteries. These cases serve as a demonstration of the potential of interdisciplinarity between supramolecular chemistry and analytical electrochemistry. With continuing efforts in research, we believe that analytical noncovalent electrochemistry will provide us with incentives in emerging applications in the fields of instrumental analysis, bioengineering and energy technology.

Electrochemical evaluation

The electrochemical evaluation was carried out using a three-electrode system controlled using a Reference 600 multipurpose instrument (Gamry Instruments) interfaced to a personal computer to record the CV and DPV data. The counter electrode and the reference electrode were a platinum wire electrode and a saturated Ag/AgCl electrode, respectively. The working electrode was a glassy carbon electrode with a diameter of 3.0 mm. The area of the working electrode was 0.071 cm². The surface of the working electrode was polished routinely using 0.05 μm alumina/water slurry on a felt surface immediately before use. All the electrochemical evaluations were performed at room temperature and in N₂-purged electrolytes. The role of N₂ is to avoid the interference of electrochemical oxygen reduction reactions, as well as to protect the formed oxygen-sensitive C^2(•+) and C⁰. The supporting electrolyte was TBAPF₆ with MeCN as the solvent. The concentration of the supporting electrolytes was 0.1 M. For the CV experiments, unless stated otherwise, the scan rate was set to 100 mV s⁻¹. Each CV measurement included three scan cycles and the second scan was plotted.

Electrochemical titration curve

Ignoring the volume change during the electrochemical titrations, we have

The binding constant K_a can be expressed as

We define

where x is a quantitative indicator to describe the titrated En equivalent, reflecting the titration process.

Rearranging the above equations, we have

According to the Nernst equation, the potential shift (Δφ) at different titration stages can be expressed as

where R is the gas constant (R = 8.314 J K⁻¹ mol⁻¹), T is the temperature (T = 298.15 K), z is the electron transfer number (z = 2 herein) and F is the Faraday constant (F = 96,485 C mol⁻¹).

Substituting equation (5) into equation (7) and rearranging gives

Accordingly, for the electrochemical titration with fixed [C]₀, Δφ is a function of two independent variables including the titration process (x = [En]₀/[C]₀) and K_a. That is, after plotting and fitting the Δφ–[En]₀/[C]₀ data, the binding constant K_a of the supramolecular complex can be obtained.

Electrochemical titration

The electrochemical titration instrument was identical to that of the electrochemical evaluation device but with a micro-syringe installed to inject the En feedstock solution into the electrolyte. Electrochemical titrations were performed in N₂-purged MeCN solutions with 0.1 M TBAPF₆ as the supporting electrolyte. A continuous N₂ flow ensures an oxygen-free environment and the consequent stability of the oxygen-sensitive C^2(•+) and C⁰ species. The C⁴⁺ solution ([C]₀ = 1 mM) was placed in the container and the En feedstock solution ([En]_stock = 50 mM) was drawn into the syringe in advance. The titrated En equivalent was controlled via regulating the injection volume of the En feedstock solution. CV and DPV evaluations were performed for each titration step. The measurement of Δφ at different titration steps is based on the peak position changes.

X-ray crystallography characterization

To grow single crystals of E2⊂2C⁴⁺, a MeCN solution of C·4PF₆ (10 mM) and E2 (2 mM) was filtered and thereafter subjected to slow vapor diffusion of ⁱPr₂O over one week, which afforded crystals suitable for X-ray crystallographic analysis. A suitable crystal was selected and the crystal was mounted on a crystal holder (MiTiGen) in paratone oil, and an XtaLAB Synergy R, DW system, HyPix diffractometer was used for data collection. The crystal was kept at 100.00(10) K during data collection. The structure was solved using OLEX2 (ref. ⁴⁴) with the SHELXT structure solution program⁴⁵ using intrinsic phasing, and it was refined with the SHELXL refinement package⁴⁶ using least squares minimization.