Entropy-driven disordered porous carbon electrodes for high-performance supercapacitors

Entropy-driven disordered porous carbon electrodes for high-performance supercapacitors | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 9 September 2025 V1 Latest version Share on Entropy-driven disordered porous carbon electrodes for high-performance supercapacitors Authors : Bolin Li , Zesheng Li 0000-0002-4238-6218 [email protected] , Changlin Yu , Qingyu Li , and Hongqiang Wang Authors Info & Affiliations https://doi.org/10.22541/au.175745720.00772911/v1 196 views 157 downloads Contents Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Entropy is a very important state function in thermodynamics, and high-entropy materials have become a hot research field in recent years. Due to the adjustable category and concentration of active components, the high-entropy mixing state, and the synergistic effect of multiple elements, high-entropy materials can provide a variety of adsorption or reaction sites, so that high-entropy materials have been widely concerned in the field of electrochemistry. In this review, we try to summarize the design principle of disordered porous carbon from the perspective of entropy driving, and formally put forward a new concept of “high-entropy carbon materials”, and summarize three design principles of high-entropy “small graphene domain”: unit entropy, ring entropy and element entropy. The unit entropy increases the system entropy by decreasing the graphene domain size and increasing the number of basic units of the system. The ring entropy is focused on the distortion of the graphene-plane six-membered carbon rings, resulting in asymmetric five/seven-membered carbon rings (5/7-membered carbon ring-based topological defects), so as to achieve the entropy increase. The element entropy is the goal of achieving high entropy by doping multiple non-metallic and metallic elements in the graphene lattice. We expect that establishing a link between entropy increase and capacitive performances will lead to novel capacitance storage mechanisms and new scientific perspectives. Entropy-driven disordered porous carbon electrodes for high-performance supercapacitors Bolin Li 1 , Zesheng Li 1* , Changlin Yu 1 , Qingyu Li 2 , Hongqiang Wang 2* 1. College of Chemistry, Guangdong University of Petrochemical Technology, Maoming, 525000, China. Corresponence author: Zesheng Li, E-mail: [email protected] 2. Guangxi Key Laboratory of Low Carbon Energy Materials, School of Chemical and Pharmaceutical Sciences, Guangxi Normal University, Guilin 541004, China Corresponence author: Zesheng Li, E-mail: [email protected] , E-mail: [email protected] Abstract: Entropy is a very important state function in thermodynamics, and high-entropy materials have become a hot research field in recent years. Due to the adjustable category and concentration of active components, the high-entropy mixing state, and the synergistic effect of multiple elements, high-entropy materials can provide a variety of adsorption or reaction sites, so that high-entropy materials have been widely concerned in the field of electrochemistry. In this review, we try to summarize the design principle of disordered porous carbon from the perspective of entropy driving, and formally put forward a new concept of “high-entropy carbon materials”, and summarize three design principles of high-entropy “small graphene domain”: unit entropy, ring entropy and element entropy. The unit entropy increases the system entropy by decreasing the graphene domain size and increasing the number of basic units of the system. The ring entropy is focused on the distortion of the graphene-plane six-membered carbon rings, resulting in asymmetric five/seven-membered carbon rings (5/7-membered carbon ring-based topological defects), so as to achieve the entropy increase. The element entropy is the goal of achieving high entropy by doping multiple non-metallic and metallic elements in the graphene lattice. We expect that establishing a link between entropy increase and capacitive performances will lead to novel capacitance storage mechanisms and new scientific perspectives. Keywords : High-entropy carbon materials, Disordered structures, Small graphene domains, Porous carbon electrodes, Supercapacitors 1 Introduction According to different energy storage mechanisms, supercapacitors can be divided into electric double layer capacitors and pseudocapacitors. The electric double layer capacitors store charge through the physical absorption/desorption of ions at the electrode/electrolyte interface, while the pseudocapacitors store charge mainly through the non-diffusion-controlled Faraday REDOX reaction of ions on/near the electrode surface [1]. Porous carbon materials (such as activated carbon, template carbon, carbon nanotubes and porous graphene, etc.) have good physicochemical stability, high specific surface, adjustable pore structure, excellent electrical conductivity and other advantages, which are currently the core key materials of commercial electric double layer supercapacitors [2]. The factors affecting capacitive performances of porous carbon-based supercapacitors often include specific surface area and pore structure of porous carbon. Particularly, the disorder of carbon structure, the size of graphene domain, carbon defect, heteroatom doping and surface chemical state are also crucial adjective [3]. In general, high specific surface area is conducive to the improvement of capacitive performance of porous carbon, but there is no strict linear relationship between specific surface area and normalized capacitance, which indicates that the pore structure will directly affect the energy storage efficiency of capacitors (appropriate pore size can improve the accessible area of ions and ion diffusion dynamics) [4]. At present, the effect of pore structure on capacitance has some common rules: micropores can provide abundant adsorption active sites for ion storage, mesoporous pores can be used as efficient channels for ion migration, and large pores can be used as storage space for ion buffer [5]. For micropores (less than 2 nm) and small mesoporous (2-5 nm), the specific capacity is optimal (for aqueous and organic electrolytes) when the pore size matches the size of the desolvated ion (or bare ion) [6]. Because of the interoperability of different pores, the hierarchical porous carbon with a suitable ratio of micro/meso/large pores will often have better capacitive properties than that with a single-size pore [7]. Remarkably, several recent major studies have confirmed that there is also a lack of sufficient correlation between pore structure and capacitance, and there are additional unknown structural variables (such as carbon structure disorder, graphene domain size, carbon defects, etc.) that affect double-layer capacitance [8-10]. A latest research published on Nature proves that carbon with smaller ordered domains (graphene domains) produce higher capacitance, that is, it is the disorder of the local structure that controls the capacitance, rather than the aperture (the smaller the graphene domains, the more disordered carbon, the higher the capacitance) [10]. For carbon with smaller graphene domains, the charge is more localized, which causes stronger interactions between ions and carbon atoms, ultimately leading to more efficient ion storage. In addition, smaller domains can lead to more topological defects (such as edge positions, pentagonal or heptagonal rings and curvature), which favor the dense packing of ions and the insertion and fixation of electrons, which can further improve the capacitive performances. The presence of surface heteroatoms (O, N, B, P, S, F) can introduce changes in the surface heterogeneity of the carbon material, thus changing the conductivity, wettability, and induced pseudocapacitance of the carbon electrode [11]. Nonmetallic heteroatom doping has been shown to be a powerful strategy to improve the overall properties of carbon materials. Among them, O and N have been extensively studied because they can act as electron acceptor/donor and control charge redistribution in the carbon matrix to enhance pseudocapacitor storage [12]. In addition, B doping has been shown to improve the electrical conductivity of carbon, while P doping can reduce electronegativity and regulate the charge distribution of carbon materials [13]. In recent years, metal single-atom doped porous carbon has also been used as a new material for high-performance supercapacitors, because metal element doping can greatly improve the electronic properties of carbon materials and optimize the ion adsorption energy [14, 15]. In recent years, the concept of high entropy has attracted much attention in the field of materials science, especially in the study of high entropy ceramics, high entropy alloys and other materials [16-18]. High entropy effect has four typical characteristics, including entropy stabilization, lattice distortion, hysteretic dynamic effect and cocktail effect. Can we apply the concept of high entropy to a porous carbon capacitive material system? The answer is yes, and the micro-structure controlling and multi-component mixing based on “entropy increase effect” is a good application direction. As entropy increases, the size of graphene domains decreases and a highly disordered carbon structure is produced, and the capacitive properties of the material also improve [10]. In addition, carbon defects cause regular graphene six-membered rings to partial deformation, resulting in disordered five-membered rings or seven-membered rings (entropy increases and favorable for electrolyte ion adsorption) [10]. In particular, the mixing entropy and structural disorder can be generated by the multi-element co-doping, and the controllable design of the pseudocapacitance of porous carbon can be realized, thus breaking through the limitations of the performance of electric double-layer materials [11-15]. In this perspective review, we propose an “entropy driven” view to try to analyze the common causes and regulatory factors of capacitance improvement of porous carbon materials by reducing structure disorder, increasing crystal atomic defect and doping mulriple heterogeneous elements. For regular graphene systems, the smaller crystal domain size means that the degree of disorder and chaos increases, and the entropy of the system will increase (here called the increase in unit entropy). Due to the defects of the crystal atoms, the order of the graphene aromatic ring is broken (the six-membered ring becomes five-membered or seven-membered ring), especially the symmetry is broken, and the entropy of the system is also increased (here called the increase in ring entropy). Multi-element co-doping increases the mixing entropy of the graphene system, which is consistent with the entropy increase concept of multi-element high-entropy alloys (here called the increase in elemental entropy). In this review, we first try to summarize the design trend of porous carbon from the perspective of entropy increase, hoping to establish a relationship between entropy increase and capacitance performance. At the same time, these improved porous carbon structures may be accompanied by novel energy storage mechanisms, which is expected to break through the limitations of traditional electric double-layer mechanisms, and bring a new perspective (see Fig. 1 for details). Fig. 1 Design principles and entropy-drive concept of porous carbon for supercapacitors. 2 Basic principles of entropy The concept of entropy (S) was proposed by the German physicist Rudolf Clausius in 1865. Originally used to describe energy degradation as one of the state parameters of matter, it has a wide range of applications in thermodynamics. Entropy is an important physical quantity in thermodynamics that describes how disordered or chaotic a system is. The thermodynamic definition of entropy is [19]: not-yet-known not-yet-known not-yet-known unknown Where T is the thermodynamic temperature of a substance; dQ is the amount of heat added to matter in the process of entropy increase, and the subscript “rev” is an abbreviation of the word reversible, indicating that the process caused by heating is reversible. Generally, the entropy can be used to evaluate the disordered process in an ordered system, that is to say, entropy is an important index to evaluate the degree of disorder in a system. The Boltzmann formula for entropy (i.e., the statistical mechanical definition of entropy) is [20]: S = k * ln (Ω ) Where S represents entropy, k is the Boltzmann constant, and Ω is the number of microscopic states in a system. The greater the number of microscopic states, the greater the entropy, the higher the disorder of the system, and the greater the “uncertainty” of the system (see Fig. 1 A for details). In contrast to Boltzmann’s entropy, Gibbs’s entropy replaces the number of microscopic states with the volume of phase space. The larger the volume of the phase space corresponding to a macroscopic state, the more uncertain the microscopic state, and the greater the entropy [21]. Therefore, entropy can be understood as “the uncertainty of the microscopic state”. The physical meaning of entropy is the measure of the disorder degree of the random particles, and the increase of entropy is the developing process from order to disorder. The process of entropy increase is a spontaneous process. The thermodynamic definition of entropy emphasize: entropy increases, the total energy of the system does not change, but the available part of it decreases. The statistical definition is that entropy measures the disorder of a system. The higher the entropy of a system, the more difficult it is to accurately describe its microscopic state. Fig. 2 Schematic diagram of entropy increase by (A) component size reducing and (B) multi-component mixing. A multielement high-entropy material is a complex mixing system consisting of five or more chemical elements mixed with each other (see Fig. 1 B for details). The core concept of its high-entropy design is to introduce local atomic disorder in the matrix, achieved by multiple elements occupying equivalent lattice positions [22]. These elements exhibit diversity in valence, ionic radius, electron configuration, and electronegativity, leading to a series of unique properties including, but not limited to, enhanced phase stability, atomic disorder due to lattice distortion, and significantly reduced diffusion rates of the elements . Multi-element doped high-entropy materials have four significant characteristics [23]: (a) High entropy effect: compared with traditional low entropy materials, high entropy materials show higher stability, which is determined by their unique entropy properties. (b) Lattice distortion: Because the constituent elements have different atomic radii, this leads to significant distortion of the lattice structure, and may even collapse into an amorphous structure in extreme cases. (c) Hysteretic diffusion: In high entropy materials, the diffusion rate of atoms is significantly lower than that of traditional materials, which has important implications for the properties and applications of materials. (d) Cocktail effect: The mixing of multiple elements not only increases the complexity of the material, but also makes it show a complex mixing effect, the so-called ”cocktail effect”, which makes the high entropy material show a richer diversity of properties . With regard to the “high entropy effect”, the following calculations can be made according to the Gibbs-Helmholtz equation [24]: ΔG mix =ΔH mix - TΔS mix Where, ΔG mix , ΔH mix and ΔS mix are free energy, enthalpy and entropy, respectively, and T is the reaction temperature. The high entropy strategy can increase the “configurational entropy” in the system and thus increase the value of ΔS mix . The expression for Gibbs free energy (G) is [25]: Where, S k , S vib , and S elec are respectively configurational entropy, phonon vibration entropy, and electron contribution to entropy. Configurational entropy S k arises from the disorder of the crystal structure. S k is particularly important in disordered multi-element systems such as metal alloys [26], solid solution compounds [27] and multi-element doped carbon materials [28]. S k is the fundamental driving force for the uniform mixing of many elements. From the perspective of thermodynamics, this phenomenon is not difficult to understand: the structural disorder caused by the solution process triggers an increase in entropy for multi-element systems. In a multi-element system, configurational entropy is a key parameter to determine whether a material is a high-entropy material (a material with configurational entropy ≥ 1.5R is usually considered to be high entropy material), which can be calculated according to the following formula derived from Boltzmann and Gibbs’ interpretation of entropy [29]: Where, S config represents the configurational entropy, R is the ideal gas constant (R=8.314 J K -1 moL -1 ), and sl1 and sl2 represent the different sublattices in the structure. x i and x j represent the mole fraction of the i and j components in their respective sublattices, and N and M correspond to the number of elements in the sublattice, respectively. High entropy materials derive their unique physicochemical properties from the intricate interactions between five or more chemically independent elements in a single phase lattice. This property opens up unparalleled opportunities for catalysis, thermoelectric applications, and electrochemical energy conversion and storage. Integrating a large number of different elements in the usual equimolar ratio in a single-phase electrocatalyst gives them a higher configurational entropy, allowing for a variety of combinations of surface interactions, thus greatly improving the activity and stability of targeted reactions [30]. For a multi-element doped carbon system, the increase of entropy means the increase of disorder. Broadly speaking, the increase in entropy of foreign elements and guest groups leads to increased confusion, and the establishment of multiple active sites through the “cocktail effect” enables unique collaborative electrochemical energy storage [31]. Due to the invasion of foreign atoms (N atoms and other heteroatoms) and the defect of C atoms, entropy increases must occur, resulting in a breakdown of order, especially symmetry, which encourages the active sites to adsorb electrolyte ions to achieve a balanced symmetrical structure [32]. These innovative design strategies significantly improve the electrochemical activity and stability, and provide experimental and theoretical guidelines for the reasonable preparation and design of high-performance supercapacitors in the future. 3 Typical cases of entropy-driven porous carbon for 3.1 Unit entropy-driven porous carbon for supercapacitors Entropy is an important concept in thermodynamics and statistical physics that describes the degree of disorder or uncertainty in the microscopic state of a system. In statistical physics, entropy is usually defined as the logarithm of the number of microscopic states of a system (as shown in Fig. 1 A ). In the nanoscience, “unit entropy” is here defined as the increase in entropy caused by the decrease in the size of basic units (such as crystal domains) of a nanomaterial, that is, the number of basic units becomes larger within a specific range. Unit entropy is closely related to the number of microscopic states and the degree of disorder of the system, and is an important bridge to describe the relationship between the macroscopic properties and the microscopic structure of the system. The process of changing from regular graphitized carbon to disordered amorphous carbon (e.g., porous carbon prepared by activating graphene with potassium hydroxide [33]) is essentially a process of increasing unit entropy (the regular flat structure of graphene becomes disordered fragments of graphene). Chemical activation of potassium hydroxide is one of the key strategies for de-graphitization and pore formation on the surface graphene-based materials. Our research group previously developed a synchronous graphitization-activation strategy and successfully prepared porous graphene with small graphene crystal domains for efficient supercapacitors [34] ( Fig. 3 A-C ). In the process of catalytic graphitization, the synchronously potassium hydroxide is introduced as a pore forming agent to activate and form pores (and also regulate the graphitization reaction kinetics). Therefore, the synchronous design of ultra-thin graphitized structure (i.e., few-layer graphene) and high specific surface area (i.e. porous graphene) is realized at the same time. The porous graphene has small graphene crystal-built porous structure and a high specific surface area of 1810 m 2 g -1 . The porous graphene has unique advantages in electrochemical supercapacitors, where the small graphene crystal domain ( Fig. 3 A ) and hierarchical porous structure ( Fig. 3 B ) endow the material with very high specific capacitances (160 F g −1 at 100 mV s −1 in organic electrolyte) and extremely high ionic diffusion kinetics (93% capacitance retention at 800 m V s −1 ) ( Fig. 3 C ). We believe that the ultra-fine graphene microcrystalline structure obtained by potassium hydroxide activation can give the material extremely high surface active sites and large ion adsorption capacity, which could be a key reason for the outstanding capacitive performances. Fig. 3 Porous graphene with small graphene crystal domains for efficient supercapacitors: (A) high resolution TEM image, (B) pore size distribution, (C) capacitive performances [34]; structural disorder determines capacitance in nanoporous carbons: (D) NMR spectrum and Δδ value-capacitance relation, (E) NMR simulations and (F) X-ray PDF analysis [10]. In general, it is generally believed that reducing the pore size of carbon materials can significantly enhance the adsorption capacity of electrolyte ions, thereby improving the capacitive performances [35]. This idea has been validated in earlier studies, especially for the use of desolvated electrolyte ions, where smaller pores have been shown to increase capacitance more effectively [36]. In addition, carbon materials with hierarchical micro-meso-macroporous structures are regarded as the best choice to improve the rate capability of organic-electrolyte supercapacitors [34]. However, in recent years, many research reports have pointed out that there is no obvious direct correlation between pore size and capacitance performances [37, 38]. In addition to the pore factor, there may be other unknown structural parameters that have an important impact on the capacitance performance. In this context, Professor Alexander C. Forse of the Department of Chemistry at the University of Cambridge conducted an in-depth study on this problem [39, 40]. They used the nuclear magnetic resonance (NMR) spectroscopy to accurately detect the structural disorder and charge storage mechanism of active carbon electrodes. The NMR spectroscopy can effectively distinguish ions in and out of carbon pores, and quantify the local structural disorder of carbon materials by measuring the chemical shift difference (Δδ value). Their a latest research from Science shows that the structural disorder of the carbon electrode is more closely related to the capacitance performance than that of the carbon pores ( Fig. 3 D-F ) [10]. Specifically, the carbon materials with more disordered structures and smaller graphene domains, showed higher capacitive properties, which provides a new perspective for the optimization of capacitor performances. The Fig. 3 D-F show the relationship between local structural disorder and capacitance of carbon materials using NMR spectroscopy. Using MAS NMR measurements, the researchers found ion adsorption in the “outer pores” and “inner pores” regions of the carbon material. The inset of Fig. 3 D shows an example of the 19F MAS NMR spectrum, indicating ion adsorption in different carbon materials. The study found a correlation between local structural disorder of carbon materials and capacitance, with carbon materials with smaller local structural disorder showing higher capacitance ( Fig. 3 D ). Using NMR simulations, the researchers also predicted the relationship between the size of ordered aromatic carbon domains and capacitance in carbon materials, showing that carbon materials with smaller ordered domains generally have higher capacitance ( Fig. 3 E ). In addition, the X-ray paired distribution function (PDF) analysis results also support the findings of NMR spectroscopy, further verifying the correlation between local structural disorder and capacitance ( Fig. 3 F ). In general, carbon materials with smaller local structural disorder generally have higher capacitance, that is the milestone conclusion the structural disorder determines capacitance in nanoporous carbons [10]. In summary, using solid-state NMR technology combined with computational simulation, the nanoporous carbon electrodes in supercapacitors can be deeply investigated. The results show that the energy storage performance of nanoporous carbon is closely related to the disorder degree of material structure. In the case of a more disorderly structure, the energy storage performance of nanoporous carbon will be significantly improved. The authors of the paper [10] believe that this is mainly because carbon materials with smaller domains have stronger interactions between carbon atoms in the ion domain, resulting in more efficient ion storage and higher capacitance. The smaller graphene domains mean more disorderly structure of nanoporous carbon, therefore, we believe that the concept of entropy can be used to describe the structure-activity relationship of supercapacitors. By increasing the disordered structure of nanoporous carbon (that is, increasing the “unit entropy” of the system), the energy density of supercapacitors can be greatly improved. The breakthrough results of this study provide new ideas and methods for the further development of supercapacitor technology, and are expected to bring greater progress in the field of energy storage. 3.2 Ring entropy-driven porous carbon for supercapacitors Graphene is a two-dimensional material made up of a single layer of carbon atoms with a unique honeycomb structure made up of six-membered rings. In graphene, the overall system exhibits a lower entropy due to its highly ordered honeycomb structure. This low entropy state makes graphene thermodynamically very stable, able to maintain its unique physical and chemical properties in a variety of environments. In the lattice structure of graphene, six-membered rings are the basic building blocks, but the presence of five-membered and seven-membered rings (namely the topological defects [41]) introduces asymmetries, which have important implications for the properties and applications of graphene. The introduction of five-membered and seven-membered rings disrupts the periodic structure of graphene, leading to asymmetry in local regions, thereby increasing the entropy of graphene (defined here as the “ring entropy”). This ring entropy increase may change the electronic structure of graphene, which in turn affects its electron density and catalytic properties. In addition, the unsaturated carbon atoms in sub-nano-pore defects of graphene may also act as active sites in graphene to promote the occurrence of chemical reactions. Single-atom layered carbon materials, such as graphene and amorphous monolayers, have inspired intense basic and applied research due to their unprecedented physical properties and broad application prospects. Introducing the topological structure of non-hexagonal elements into a honeycomb lattice to form a five-, six-, and seven-membered (5-6-7) ring hybrid structure can significantly alter the electronic and mechanical properties of sp 2 carbon networks, thus providing adjustable properties similar to those of disordered hyperhomogeneous systems [42]. At the same time, internal defects in the graphene plane, such as pentagons and pore edges, can also induce asymmetric charge/spin redistribution, thereby increasing electrochemical activity ( Fig. 4A-C ) [43]. In typical cases, these intrinsic defects are shown to be more important than dopants in activated porous carbon materials, highlighting the need for in-depth study of this emerging source of electrochemical activity. It has been well demonstrated that the small-area sp 2 -hybrid graphene nanosheets (high unit entropy) often retain a large number of topological defects (high ring entropy), which prove to be the true electrochemically active sites for many applications. not-yet-known not-yet-known not-yet-known unknown Fig. 4 Small-area sp2-hybrid graphene nanosheets with topological defects: (A) anti-FFT filter TEM image (hexagons and pentagons are marked with yellow and red respectively), (B) EPR spectrum (carbon defect characterization), (C) defect structure schematic diagram [43]; Intrinsic defects enhanced ion adsorption and induce additional double layer capacitance: (D) porous carbon with different defects, (E) DFT calculation for ion adsorption and electron density, (F-H) capacitive performances [45]. In general, when amorphous carbon is prepared by chemical etching, it can induce the formation of carbon intrinsic defects, such as a large number of positive topological defects (five or six membered rings) in the corners of the surface [44]. Topological defects of carbon materials are usually caused by bending or squeezing of six-membered aromatic rings. This unique deformation gives carbon structures some new properties. Recently, researchers have shown that abundant intrinsic defects can form additional double layer capacitors and improve the adsorption capacity of electrolyte ions (Fig. 4D-H ) [45]. From Fig. 4D, it can be seen that there are a large number of twisted lattices with varying degrees of deformation, which leads to the formation of a special ”river”-like structure. These lattice deformations indicate the production of a large number of intrinsic defects in carbon, which can serve as active sites for improving capacitive properties. At the same time, there are many porous structures, folds and edges, indicating that a large number of edge defects have been formed. Such fully exposed interconnected intrinsic defects can act as ion transport channels and effectively facilitate ion storage. The influence mechanism of intrinsic defects on capacitance is elucidated by density functional theory (DFT) calculation. In Fig. 4E, the adsorption energy of Na ions in the most stable configuration of graphene with different defects is calculated. Compared with pure graphene (Eads=-0.11 eV), the adsorption energies (Eads) of defect types 1~4 are -0.78, -1.02, -1.23 and -1.45 eV, respectively. The existence of intrinsic defects will greatly enhance the adsorption capacity of Na ions. In addition, through charge density calculation, it is proved that graphene with higher intrinsic defect content has stronger sodium storage capacity. Due to the low charge density at the defect, the charge transfer of sodium ions to carbon atoms is relatively easy. The charge is transferred from the Na ion to the nearest carbon and accumulates at the intrinsic defect site of the carbon. The presence of intrinsic defects breaks the original charge balance of pure graphene, resulting in a more obvious charge transfer, which promotes the charge density redistribution and further promotes the adsorption of Na ions. In Fig. 4F, the CV curve of the carbon electrodes is quasi-rectangular, exhibiting typical double-layer capacitance (EDLC) behavior. In addition, the DT-PC sample with the highest intrinsic defect content has the largest CV integral area, indicating the best capacitive performance. At a speed of 2 mV s-1, the DT-PC sample has the highest specific capacitance of 181 F g-1 compared to ST-PC (130 F g-1 ), AC (107 F g-1 ), and NT-PC (21.4 F g-1) (Fig. 4G ). According to the literature, the theoretical double layer capacitance of carbon is about 20 μF cm-1 [46]. The specific surface area of DT-PC is 588 m2 g-1, and the corresponding theoretical EDLC is 117.6 F g-1. However, the actual specific capacitance of 181 F g-1 is much higher than its theoretical value, indicating that there are other active sites for ion adsorption besides the specific surface area. The oxygen-containing functional groups in carbon materials can contribute a certain pseudocapacitance in reversible redox reactions. In order to evaluate the contribution of intrinsic defects to capacitance, the Dunn and Trasatti methods were used to divide the total capacitance at several scanning rates into double layer capacitance and pseudocapacitance, and the contribution of the latter is much smaller than that of the double layer capacitance (Fig. 4H ). The actual EDLC is much higher than the theoretical capacitance value derived from the specific surface area, and the additional EDLC can be attributed to abundant intrinsic defects of 6-C ring (namely the high “ring entropy”). These intrinsic defects induce the local charge density rearrangement and lattice deformation of the carbon, thus providing rich active sites for ion adsorption and enhancing its capacitive properties. 3.3 Element entropy-driven porous carbon for supercapacitors In recent years, the research of multi-element co-doped graphene materials has gradually emerged, especially its application in high entropy capacitors, which has shown great potential [47]. To achieve a variety of elements (such as nitrogen, oxygen, sulfur, phosphorus, boron, etc.) co-doping graphene is a very meaningful and challenging task. The co-doping process can not only regulate the electronic structure of graphene, but also introduce more active sites, thereby improving its electrochemical performances. When five or more elements are doped, these elements show a uniform distribution in the porous carbon material, which can achieve high entropy characteristics (named as “element entropy”). This multi-element, disordered structure gives porous carbon materials unique physical and chemical properties (such as good electrical conductivity, electronegativity, redox reactivity, etc.). The application of multi-element co-doped high-entropy carbon in supercapacitors can further improve the overall electrochemical performance of devices. The application of non-metallic element doped carbon materials in supercapacitors can significantly improve their pseudocapacitance performances. For example, nitrogen doping can introduce additional charge storage sites and improve pseudocapacitance performances (Fig. 5 A-C ) [48]. The doping process usually involves methods such as high-temperature heat treatment or chemical vapor deposition to ensure that nonmetallic elements are uniformly incorporated into the disordered structure of the carbon matrix (Fig. 5 A ). The nitrogen doped structure can also be further confirmed by XPS spectrogram (Fig. 5 B ). Nitrogen-doped carbon materials exhibit higher specific capacitance (often with reversible REDOX peaks) (Fig. 5 C ) and high energy density in supercapacitors, while maintaining good power density. Since the electronegativity of nitrogen (χ=3.04) is higher than that of carbon (χ=2.55), the doping of nitrogen will produce polarization in the sp2 hybrid lattice of carbon materials, thereby speeding up the rate of electron transport and improving the power performance of capacitors [47]. In addition to the common pseudocapacitance, different non-metallic elements also play different modifying roles in carbon materials. For example, boron, with its unique three valence electron properties, can act as an electron acceptor and lead to an imbalance in the charge distribution within the graphene lattice, thereby optimizing its electrochemical performance. In this process, boron doping is accompanied by the introduction of oxygen atoms, resulting in the formation of BC3, BC2O and BCO2 three unique structures. The functional groups contained in these boron-oxygen structures can effectively improve the hydrophilicity of graphene. For phosphorus doping, C-P bonds inside graphene can change the charge and spin density distribution of carbon, adjust the band structure of graphene, and thus enhance its electrochemical activity. Phosphorus at the edges of graphene induces the formation of oxygen-containing groups such as C-O-P bonds, C-P-O bonds and C-P=O bonds, which can also improve the hydrophilicity of graphene [47]. In summary, the multiple non-metallic elements doped in the lattice of the carbon materials can play synergistic effects and greatly improves the capacitive performances (including the EDLC and pseudocapacitance) of high-entropy carbon electrodes. Fig. 5 Nitrogen doping introduce pseudocapacitance performances: (A) TEM image (disordered defective carbon structure), (B) XPS spectrum (N doping characterization), (C) capacitive performances [48]; Coupling multiple doping active sites and carbon defects: (D) structural model, (E, F) capacitive performances, (G) DFT calculation, and (H) AZICs [49]. The synergistic effect of multi-element doping (increasing element entropy) and carbon structure defects (increasing ring entropy) has been shown to effectively improve the microstructure of carbon materials, enhance the charge adsorption and storage sites, and thus significantly improve the charge storage capacity and mass and charge transfer kinetics of carbon materials. Recently, Li et al. explored the coupling between multiple active sites and carbon defects, and revealed the mechanism by which coupling enhances the capacitance and power characteristics of aqua zinc-ion capacitors (AZICs) with ZnSO 4 electrolyte ( Fig. 5 D-H ) [49]. N, S co-doped multiple active sites and carbon topological defects (five-membered rings) provide abundant charge storage sites and enhance charge transport capacity ( Fig. 5 D ). The abundant nanopore structure (average 2.2 nm) will facilitate the rapid migration and transport of charge carriers (SO 4 2- ) in the carbon material structure. The high ratio of diffusion contribution to capacitance contribution at different sweep speeds (5~100mV s -1 ) further demonstrates its fast capacitor dynamics ( Fig. 5 E and F ). According to the DFT calculation, the coupling of N and S active sites and carbon holes significantly improves the adsorption energy of SO 4 2- on carbon materials, and realizes the rapid reversible adsorption of charge carriers on the surface of carbon materials ( Fig. 5 G ). By assembling the optimized material into AZICs devices, the energy density (164.1 Wh kg −1 ) and power density (30.1 kW kg −1 ) were demonstrated ( Fig. 5 H ). This work can not only provide theoretical guidance for the construction of dual entropy-increasing porous carbon materials with excellent structural properties, but also lay an important foundation for the application of capacitive porous carbon materials in AZICs. 4 Concept statements of high-entropy carbon materials The scientific significance of entropy, as described by the Boltzmann entropy equation, is that it reflects the equilibrium probability of a state. That is, when a certain amount of energy is introduced into the system, a certain number of basic units can be randomly arranged into an infinite number of configurations, while the high entropy property focuses on the disorder and stability of the system [50]. Therefore, when the graphene domains of the carbon materials become smaller, the number of basic units increases significantly, and these very small graphene units can form a stable system, we can consider these disordered carbon materials to have high entropy properties (so-called “unit entropy”). According to the Boltzmann equation S=klnΩ, the probability of microstate occurrence (Ω) is related to the thermodynamic properties of the system. The increase in the number of graphene units can be refined into the microscopic diversity (W) of carbon structure, including the transformation of six-membered rings into irregular five-membered or seven-membered rings and the formation of carbon vacancy defects (so-called “ring entropy”), but also the doping of multiple nonmetallic elements (so-called “elemental entropy”). Therefore, we propose a new definition of “high-entropy carbon material”: A high-entropy carbon material is a stable system consisting of an infinite number of small-sized graphene units doped with at least five or more elements and rich in intrinsic carbon defects. The mixing entropy of these disordered multi-element defect-rich graphene fragments can be described by the equation S=klnW. Recently, the latest research in Science by Liu et al. revealed that there is a close relationship between the microscopic disorder of porous carbon materials and capacitance, which is essential for the design of electrochemical energy storage devices with high energy density [10]. Using NMR spectroscopy and simulation studies, they found that disordered carbon materials are able to store ions more efficiently and thus increase capacitance due to their smaller “graphene domain” (we call the “basic unit” in this review). The size of “graphene domain” in the nanopores (i.e. the average size of the graphene fragments inside the pores) has a significant effect on the capacitance. Here, we believe that the increase of “unit entropy” in high-entropy carbon materials plays a key role. In a nanopore of the same size, the smaller the size of “graphene domain”, the more basic units, and the greater the “unit entropy” in the pore. The tiny graphene units are arranged in uncertain directions and distributed steadily inside the carbon pores (see Fig. 6 ). Such disordered high-unit-entropy carbon structure greatly increases the adsorbated amount of electrolyte ions on the wall of nanopore, thus greatly improving the capacitive storage capacity of porous carbon materials. Fig. 6 Samll “graphene domain” in the carbon nanopores. In the construction of small-sized graphene fragments with minimal “graphene domain” units, the high temperature chemical activation strategy is often used, which often leads to the formation of abundant intrinsic defects (including carbon vacancy defects (such as single and multi-vacancy defects) and topological defects (such as five-membered rings and seven-membered rings) and edge defects (unsaturated coordination carbon atoms) in the small graphene units (see Fig. 7 ). Defect engineering can lead to the loss or lattice distortion of carbon atoms (that is, an increase in “ring entropy”), while producing an abundance of unsaturated carbon atoms as efficient and additional ion adsorption sites. In addition, by changing the hybrid orbital type of carbon atoms [51], the synchronous introduction of foreign heteroatoms (including non-metals (N, O, B, P, S, etc.) and metal atoms (Ru, Mn, Ni, etc.) (that is, an increase in “element entropy”) can produce rich non-intrinsic defects (heteroatom-induced external defects) on the surface of carbon materials. Finally, these various intrinsic and external defects provide abundant active sites for improving reversible ion adsorption or redox reaction capacity. In view of this, porous carbon materials with abundant intrinsic and external defects and rich heteroatomic groups are of great importance for significantly enhancing the capacitance under the same specific surface area and pore structure. Fig. 7 Samll graphene domain with abundant defects and rich foreign heteroatoms. The capacitive properties of carbon materials can be effectively enhanced by heteroatom doping, mainly for the following reasons: 1) heteroatom doping can effectively regulate the electronic structure and intrinsic properties of graphene units, provide effective redox active sites, and improve electrochemical reaction kinetics; 2) Heteroatoms give new electronic energy levels and change the charge distribution of carbon, which greatly improves the electrical conductivity of carbon materials; 3) Heteroatom doping can produce additional defects and micropores, which promotes the rapid diffusion of electrolyte ions [52]. Due to the interaction between multiple atoms, multi-element doped high-entropy carbon materials can store more energy based on the Faraday reaction mechanism. The REDOX potential of a single doped element is fixed, while multiple doped elements have multiple and continuous REDOX pairs, which can enhance charge storage capacity and improve capacitive energy density (see Fig. 8 ). This is precisely an advantage of high-entropy electrode materials used in supercapacitors [53]. Different atomic combinations can trigger a variety of unique synergistic mechanisms, and in-depth exploration of these mechanisms is essential to elucidate the underlying mechanism of electrochemical performance improvement. Fig. 8 Continuous REDOX pairs for multi-element doped carbon materials. In the traditional concept, the design principle of porous carbon for supercapacitors include: (1) Increasing specific surface area (i.e., available/ionic accessible pore area); (2) Optimizing pore size distribution (such as disordered/regular pores, micropores, mesopores and macropores, hierarchical pores); (3) Regulating carbon structure (such as sp 2 carbon content, ordered domain size, carbon atom vacancy, foreign element doping); (4) Regulating ion adsorption state (including electron state density and adsorption energy); (5) Enhancing ion/electron transport dynamics (ion and electron bi-channel design). Usually, the energy characteristics of supercapacitors is mainly determined by (1) and (3), while the power characteristics is mainly determined by (2) and (3). In general, the above design strategies have been widely studied and discussed over the past decades, and have made important contributions to the development of supercapacitors. At the moment, the disorder of the carbon structure is proved more crucial (even a decisive factor) for capacitive performance: (1) Ordered domain size (the size of graphene units) (the smaller the size, the higher the disorder); (2) Carbon atom vacancy (in-plane defects on graphene units) (the denser the vacancy, the higher the disorder); (3) Foreign element doping (nonmetal and metal atoms doping) (the more the doping atoms, the higher the disorder). The basic principles of entropy-driven disordered porous carbon electrode (made from the high-entropy carbon materials) mainly includes three aspects: (1) The smaller the size of the graphene units in pore walls, the higher the disorder of porous carbon (i.e., the “unit entropy” is increasing); (2) Carbon atom vacancy on small graphene units resulting in deformation of the aromatic rings (i.e., the “ring entropy” is increasing) (3) Nonmetal/metal atoms doping generating a multi-element complex graphene system (i.e., the “element entropy” is increasing). For the “samll graphene domain” with abundant defects and rich foreign heteroatoms, the three high-entropy principles (namely the “unit entropy”, “ring entropy”, and “element entropy” ) could be integrated and mutually reinforcing. The specific triple synergistic mechanism needs further experimental and theoretical proofs for the time to come. 5 Opportunities and challenges This paper reviews several important cases of improving electrochemical energy storage performance by increasing material disorder, and tries to find out the correlation between them. We propose the idea of “entropy driven” and try to analyze the common causes and regulatory factors for the increase of porous carbon material capacitance. Entropy is a descriptor of disorder, and disorder is a key parameter to define the performance of supercapacitors, so entropy has great relevance in regulating electrochemical performance. Defects and heteroatoms can induce stronger physical or chemical adsorption of electrolyte ions. Metal atoms can also catalyze REDOX reactions. Therefore, these parameters help to improve the energy storage of supercapacitors. In fact, the relationship between entropy and carbon defects, doping, electronic properties, ionic adsorption, or electrochemical property requires in-depth study. Here are some of the key challenges: (1) We need to further emphasize the role of entropy in explaining various entropy-driven capacitance improvement mechanisms. For example, 1) KOH activation usually leads to an increase in specific surface area and thus an increase in material capacitance. The relationship between KOH activation and entropy increase requires in-depth exploration of the change from ordered structure to disordered structure; 2) The situation of multi-element doping to increase capacitance needs to be further analyzed by referring to the application principle of high-entropy alloys and high-entropy oxides in electrochemical energy storage. Units, rings, or elements are important to the electronic structure of carbon and therefore affect the performance of supercapacitors, and further and comprehensive experimental studies and characterization are needed to correlate the structural or capacitive properties of high-entropy carbon. (2) The quantitative relationship between entropy increase and electrochemical capacitance performance needs further exploration. The linear relationship between the properties of high-entropy disordered carbon materials and the number of defects needs scientific proof. The entropy increase of five-membered and seven-membered rings should be further quantified from the perspective of asymmetric structure and odd carbon rings. In addition, there are two competing requirements for energy storage in supercapacitors. One is rich in active sites, which can achieve ion adsorption or REDOX reactions by introducing defects and heteroatoms. The other is rapid electron transfer, which requires continuous graphite structures at relatively long scales. This is a key reason for limiting the number of defects and heteroatoms in the carbon framework. In high-entropy supercapacitors, a basic balance is required to provide optimal performance. (3) The capacitive properties of carbon electrodes are influenced by the complex interaction of carbon structure (such as disorder, pore size, pore volume, and surface functional groups) with the electrolyte (including solvents and ions) under polarization. Therefore, while discussing the entropy of the electrode, we also need to consider the interaction of high-entropy carbon with the electrolyte. The disordered structure of high-entropy carbon can significantly affect ion interactions, dissolvation (coordination) and confinement effects. In addition, heteroatom doping, known to enhance capacitance, can also improve electrolyte wetting and alter ion adsorption mechanisms, factors that need to be fully investigated in future studies. In thermodynamics, the energy storage system must be analyzed as a whole, including exploring the design principle of the high-entropy electrode, as well as the interaction mechanism between the electrode and the electrolyte. 6 Conclusions and prospects 6.1 Conclusions The concept of high entropy is often used in materials science to describe alloys or compounds that have multiple elemental compositions and similar amounts of each element. In this review, the concept of high entropy is formally introduced to carbon materials to describe graphene-based carbon structures with multiple defect types and multiple element distributions. Such high-entropy, small-size graphene domains may have more complex electronic structures and properties, opening up new possibilities for electrochemical applications of graphene carbon materials. In summary, the small ordered domains, five-membered rings, seven-membered rings, asymmetries, multi-element doping, defect, and high entropy concepts in graphene are interrelated, and together they affect the electrochemical properties of graphene and the application of supercapacitors. Based on the entropy increase perspective of high-entropy carbon materials as an improved strategy for the preparation of new capacitive carbon, it mainly leads to changes in geometry (domain size and topological defects), chemical composition (multi-element doping) and electronic structure (electron density and orbital hybridization), which optimizes the adsorption behavior of electrolyte ions and enhances the REDOX kinetics, ultimately boosting the capacitive storage capacity of the carbon materials. High entropy carbon materials have sufficient active sites, low ion diffusion barrier, fast ion adsorption and mass transfer kinetics, improved interfacial charge transfer, enhanced structural stability and reversible Faraday charge transfer. By designing the small ordered microstructure, intrinsic/external defects and high electrochemical activity of porous carbon, we can construct new high-entropy disordered porous carbon electrodes for high energy density supercapacitor applications. 6.2 Prospects The key strategy of high-entropy carbon materials is to produce highly disordered microscopic structures by reducing graphene size, forming carbon defects, and introducing multiple elements, thus giving the material unique electrochemical properties. The essence of the high entropy concept lies in the creation of highly complex and disordered structural states at the atomic or molecular level by increasing the type and number of components, thereby significantly changing the properties of the material. Therefore, in the future research, how to efficiently reduce the graphene domain size of porous carbon and increase the number of basic units while ensuring the stability of carbon materials is particularly critical. Our previously proposed combined preparation strategy of “simultaneous graphitization and chemical activation” may have a complementary advantage of high activity and stability [34]. Using a number of high-entropy molecules as carbon preprecursor, such as Azulene, a class of non-benzene aromatics composed of electron-rich five-membered rings and electron-deficient seven-membered rings, there is an opportunity to design disordered carbon structures rich in topological defects [54]. In particular, the occupying distribution of polymetallic elements on the carbon lattice at the atomic scale provides a new idea for the design of high-entropy carbon materials (namely carbon-based high-entropy single atoms) [55]. Despite the advantages of high-entropy carbon, some key problems still need to be further solved: 1) Establish quantitative relation of capacitive properties and entropy; 2) Unify the dynamics and thermodynamics of the electrode process; 3) Reveal the synergistic mechanism of the three types of high entropy principles; 4) Accurate characterization of high entropy structures at the atomic level; 5) Improve the stability of high-entropy carbon; and 6) Promote the industrial application of high-entropy carbon. 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Keywords disordered structures high-entropy carbon materials porous carbon electrodes small graphene domains supercapacitors Authors Affiliations Bolin Li Guangdong University of Petrochemical Technology View all articles by this author Zesheng Li 0000-0002-4238-6218 [email protected] Guangdong University of Petrochemical Technology View all articles by this author Changlin Yu Guangdong University of Petrochemical Technology View all articles by this author Qingyu Li Guangxi Normal University View all articles by this author Hongqiang Wang Guangxi Normal University View all articles by this author Metrics & Citations Metrics Article Usage 196 views 157 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Bolin Li, Zesheng Li, Changlin Yu, et al. Entropy-driven disordered porous carbon electrodes for high-performance supercapacitors. Authorea . 09 September 2025. 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