Conductivity and interaction mechanism of polydopamine-graphene oxide: A combined experimental and density functional theory investigation

The electrochemical activity of electrode material plays an important role in enhancing energy storage e�ciency in �ow batteries (FBs). Polydopamine (PDA) mixed with graphene oxide (GO) exhibited improved performance. However, few studies investigated on the interplay between DA and GO, particularly the in�uence of GO's functional groups on its adsorption e�cacy. In this study, the prepared PDA-GO composites were formed by a straightforward and eco-friendly approach. The impact of the PDA on GO's electrical conductivity and the ratio of the DA-to-GO was explored. Furthermore, the impacts of various oxygen-containing functional groups on the adsorption DA process of GO were thoroughly explored using density functional theory (DFT) calculations. Focusing on the adsorption energy, charge density difference, energy gap, and reaction barrier. PDA-GO exhibits the strongest electrical conductivity where the addition ratio of DA-to-GO is 1:2. PDA partially reduction the GO in the process of combining with GO, and the layer spacing increases. DFT calculations indicated that the reduction of DA to GO happens mostly in the epoxy groups, and the basal plane of PDA-GO remains reasonably intact, while the conductivity is greatly improved by the binding of DA to the epoxy groups. DA molecules tend to align parallel to the graphene sheet during the optimization process. The results suggest that a portion of DA molecules in�ltrate the interlayer of GO, engaging in π - π and hydrogen bonding interactions with GO during the preparation phase. On the other hand, the epoxy group signi�cantly destroys the π - π interaction between GO and DA, resulting in a reduction in the adsorption energy between the two, whereas the remaining functional groups enhance both. However, the augmentation of the DA adsorption energy by the hydroxyl groups on the surface of the GO is dramatically diminished when the hydroxyl groups on GO reach a particular density owing to the breakdown of the π - π interaction. This study serves as a theoretical foundation for the selective synthesis of PDA-GO composites and fresh ideas for their further utilization in electrode materials.


Introduction
Energy serves as the fundamental cornerstone for socioeconomic, scienti c, and technological development and is indispensable for global economic growth.Flow batteries (FBs) has gained signi cant traction in the eld of energy storage technology due to their intrinsic advantages, including safety, dependability, long life, and high e ciency.The electrode, as the primary location of electrolyte ion redox reaction in FBs, is critical, and the electrochemical activity and surface morphology of the electrode material directly impact the energy storage e ciency of FBs [1].Due to their superior electrical conductivity and durability, porous carbon-based materials such as graphite felts (GFs) are now commonly employed as electrodes in FBs systems.However, GFs have a low speci c surface area, poor electrochemical activity, hydrophilicity, and reversibility, and catalytic mediators deposited or grown on GF electrodes are prone to be peeled off by electrolyte scouring, resulting in the loss of electrochemically active potentials and affecting FBs performance [2][3][4].To enhance their electrochemical performance and surface activity, these carbon-based electrodes must be modi ed.
There are various carbon-based electrode modi cation approaches available at the moment to increase the electrochemical performance of FBs.The representative methods include mainly metal/metal oxide modi cation, nonmetal atom modi cation, and defect engineering for graphite felt.Dopamine (DA) may be converted into polydopamine (PDA) through a simple self-polymerization reaction [5].It may be employed as a functionalization platform for most materials, enhancing the mechanical characteristics of the substrate material while offering an abundance of active sites for modi cation of the desired molecules [6][7][8].Ji [7] employed carbonized PDA as an immobilization medium to improve the stability and electrochemical catalytic activity of Mn 3 O 4 nanoclusters on electrode materials.Graphene oxide (GO) is widely used in polymer composites and electrode materials due to the introduction of a large number of oxygen-containing functional groups at the edges and basal surfaces of monolayer graphene, which makes it easy to improve the material's properties through synergistic effects with other materials via covalent bonding, hydrogen bonding, π-π interactions, etc [9,10].Due to the PDA structural fragment's rich π-electron cloud, it can have π-π interactions with GO [11], and the amino group in PDA can form covalent connections with the oxygen-containing groups in GO.Furthermore, the process of PDA functionalization of GO is followed by GO reduction, generating reduced GO while enhancing electrical conductivity, and PDA coated on the surface of GO can promote GO dispersion [5,12,13].Jeremiah Amesimeku [5] employed PDA/GO coating to improve the surface conductivity of aramid textiles, and as the number of coatings rose, so did the connectivity of GO on the surface of the aramid, and the conductivity improved even more.Yu [10] employed PDA as a bonding layer to alter GO in the fabrication of composite dielectric material, and the dielectric properties of composite material are signi cantly enhanced due to the interfacial polarization of PDA.Previous research has shown that DA has a distinct advantage in increasing the electrical conductivity of GO, whereas surface oxidation of GO destroys the graphene lamella, affecting the π-π interactions between DA and graphene akes.However, there are few studies investigate the interactions between DA and GO, and the nature of their bonding sites is not clear.
This study combines a mix of experimental characterization and DFT calculations to conduct in-depth investigations on the two's interaction at the molecular level and give theoretical references for future applications of DA and GO.GO was synthesized using a modi ed Hummer method, and PDA-GO composites were prepared by altering the DA-GO composite ratio.Scanning electron microscopy (SEM), Fourier-transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), Raman, and another characterization method, as well as electrochemical property tests, were utilized to examine the bonding mechanism of DA and GO, as well as the effect of DA on the electrochemical characteristics of the composites.Furthermore, DFT was used to explore the interaction between DA and GO at the microscopic level and the in uence of various oxygen-containing functional groups on GO for the interactions between GO and DA [16,21].In detail, we perform the above analysis by calculating the adsorption energies [22], charge density difference [23], reaction barrier [24,25], and the HOMO-LUMO energy gaps of the different models after modeling the adsorption of DA by GO containing various types of oxygen-containing functional groups.
1.2 Improvement of the Hummers method for the preparation of GO At rst, 2 g of squamous graphite was weighed with an electronic balance and placed in a 500 mL beaker; 100 mL of concentrated H 2 SO 4 was added under ice bath conditions and vigorously stirred for 15 min; 12 g of KMnO 4 was slowly added into the mixture, and stirring was continued for 15 min, yielding a dark green solution.Subsequently, the beaker was put in a constant temperature water bath at 45°C, and the stirring time of the medium temperature water bath was set to 2 h, yielding the brown solution.After the medium temperature reaction, 50 mL of deionized water was added to the mixed solution, and the temperature was naturally increased to 95°C after stirring.Then, 50 mL of distilled water was added 15 min later, and 2 mL of hydrogen peroxide was added after the high-temperature reaction.The color of the solution changed to bright yellow, indicating that the GO had been successfully prepared.Finally, the combined solution was deionized, washed to neutral, and ultrasonicated for 1 h.The combined solution was placed in a centrifuge and spun at 4000 r/min for 10 min.The precipitate was rinsed and centrifuged multiple times with deionized water before being dried at 90°C for 24 h to obtain a dry GO sample.

PDA-GOn composite preparation
A 10 mM Tris-HCl buffer solution was formed by adding 0.242 g Tris and 200 mL of deionized water to a 500 mL beaker, and the solution was kept at pH ≈ 8.5 by adding HCl at room temperature.Continuous sonication was used to disperse 100 mg GO in the buffer solution for 1 hour at 30°C to make GO uniformly dispersed.Then, 50/66.67/100/150/200mg of DA hydrochloride was added to the Tris-HCl buffer solution containing GO and mixed well before being stirred at 30°C for 24 h.The mixed solution was placed into a centrifuge and spun at 11000 r/min for 10 min.The precipitate was rinsed with deionized water and repeatedly centrifuged before being dried at 50°C for 24 h.The dried PDA-GOn samples were obtained, which were named PDA-GO 2:1 , PDA-GO 1.5:1 , PDA-GO 1:1 , PDA-GO 1:1.5 , and PDA-GO 1:2 .A schematic of the PDA-GO composites' manufacturing process is shown in Fig. 1.

Material preparation for electrodes
The electrochemical characteristics of the composite materials were analyzed and tested using a CHI650E electrochemical workstation.The following is the procedure for preparing the three-electrode system: 1 mg composite material was coated on nickel foam (1 cm×1 cm) and crushed for 30 seconds using a tablet press at a pressure of 10 MPa.Saturated calomel electrode (Hg/HgO) and platinum mesh electrode were utilized as reference and auxiliary electrodes, respectively, with 2 M KOH as the electrolyte.

Calculation method
In this study, to better understand the interaction mechanism between PDA and GO.In Fig. 2, we relaxed the shortened structures of the GO and PDA components.It should be highlighted that their structures are reprehensive of PDA and GO reducing the computation costs and nevertheless providing valid results [16][17][18][19][20]. Our major purpose is to analyze the role of van der Waals/electrostatic forces at the interface between the DA and GO.The GO model was constructed using the (001) crystalline surface of graphite and was expanded cellularly to form a 5×5 graphene lamellar structure containing 70 C atoms as the starting structure.On this basis, the remaining GO models have various types of oxygen-containing functional groups, including hydroxyl (-OH), carboxyl (-COOH), epoxy (-C(O)C-), and carbonyl functional groups (C = O), with hydrogen saturation of the graphene edges.Prior to adsorption, the structure of DA was individually optimized as a model construct for adsorption with GO.Calculations were carried out using a Gaussian-09 [26] software package based on DFT.The structural optimization of GO adsorbed DAs with various types of oxygen-containing functional groups was initially performed in a computational technique employing the B3LYP method [27,28] in conjunction with the 6-31G* [29,30] basis set.Subsequently, each structural model was further improved by adding the GD3BJ [31] dispersion correction based on the B3LYP method and combining the 6-31 + G* [32,33] basis set with the additional polarization function.Furthermore, the frequency was added to the calculation to ensure that the optimized structure was at the lowest energy, and the energy convergence criterion was 1×10 − 6 eV.The optimized structure was used for single-point energy calculations.The optimized structure was subjected to wave function analysis using Multiwfn software [34] to obtain the density of states, charge density difference, and other data, while the charge density difference of the related structural model was plotted using VESTA software [35].The adsorption energies (E ads ) were computed using Eq. ( 1).The charge density difference (∆ρ) after binding is computed by Eq. (2).
where E AB represents the total energy of DA adsorbed on GO, E A stands for the entire energy of GO, and E B denotes the total energy of DA.
where ρ AB stands for the charge density of GO bound to DA, ρ A represents the charge density of GO, and ρ B is the charge density of DA.

Structural models
We model the adsorption with graphene structure S0 as the substrate and add different types of oxygencontaining functional groups on S0 as an initial structure for relevant calculations to better investigate the interactions between different types of oxygen-containing functional groups contained on GO and DA.The content of other types of functional groups is comparatively low because oxidants, acidic conditions, and heat treatment during the preparation of GO will lead to the appearance of hydroxyl functional groups on the surface of GO.Considering the calculation costs and the reduction of interactions between functional groups, highlighting interactions between GO and DA containing speci c functional groups, the number of different types of oxygen-containing functional groups is set to one.Geometrical structures S1-S8 are established as illustrated in Fig. 2, where the starting states of DA and GO are parallel in structures S0-S4, and DA is put at the edge of GO in structures S5-S8.Furthermore, the amino/hydroxyl groups of DA are relative to the GO edge functional groups, respectively, and the structures in which the amino groups relative to GO are referred to as S5n-S8n.In addition, to explore the in uence of the number of hydroxyl groups on graphene on the interaction between DA and GO, the geometrical structures S9-S12 were constructed, each re ecting the presence of 2-5 hydroxyl groups on graphene.According to Kittiya et al. [20], the hydroxyl groups are distributed in an energy minimum con guration.The geometrical composition of structures S1-S12 is shown in Table 1.To explore the reduction of GO by DA, as illustrated in Fig. 3, the ring-opening reaction of the DA amino group to the epoxy group of the GO base surface is referred to as reaction , and the dehydration condensation with the carboxyl group at the GO edge is referred to as reaction .In reaction , DA undergoes a ring-opening reaction with the epoxy group on the surface of GO, and the epoxy group's C-O bond is broken.An N-H bond on the amino group of DA is also cleaved; the H atom is transferred to the site where the C-O bond is broken, forming a new hydroxyl group, and the N atom of DA and the C atom of the epoxy group form an N-C bond binding DA to GO.In reaction , DA undergoes amidation with the carboxyl group at the edge of GO, the -OH released from the carboxyl group forms a water molecule with the H atom released from DA's amino group, and the formed amide bond binds DA to GO. Results and discussion

Cyclic voltammetry testing
In this paper, the DA/GO ratio was varied during the preparation of PDA-GO composites to investigate the effect of DA on the electrochemical properties of the composite electrode materials and to explore the advantages of PDA-GO in promoting electrical conductivity over pristine GO.The cyclic voltammetry (CV) graphs of GO and PDA-GO samples are shown in Fig. 4, and Table 2 displays the peak current difference (△Ip), peak potential difference (△Ep), and peak current ratio corresponding to the CV graphs.The peak current difference can re ect the material's electronic and ionic conductivity, and the peak current ratio can give information about the material's reversibility, with a ratio closer to 1 indicating better reversibility.
As shown in Fig. 4, the addition of DA to GO resulted in a negative shift of the oxidation peak and a positive shift of the reduction peak, and △Ip seemed to rise greatly, demonstrating that DA can improve GO conductivity.With the growing DA to GO ratio, the magnitudes of △Ip variation are 4.146, 3.120, The peak current ratio of the PDA-GO 1.5:1 sample is 1.435, indicating better reversibility, but at this ratio, the △Ip is low, which suggests worse conductivity than the PDA-GO 1:2 sample.
The electrode material of a liquid ow battery should inherently possess great conductivity and reversibility, and the DA/GO ratio of 1:2 shows distinct advantages in terms of conductivity and reversibility over other ratios.The degree of polarization of the reversible reaction system can also be re ected from the CV diagram, with a smaller △Ep of the redox peak, indicating a less signi cant polarization phenomenon.The extents of △Ep change were 0.068, 0.074, 0.074, 0.082, 0.074, and 0.070 (V), and the polarization of the composites varied gently with the increase of the DA to GO ratio, with the PDA-GO 1:2 samples exhibiting the minimal polarization.In summary, PDA-GO composites with a DA/GO ratio of 1:2 perform well as electrode materials.

SEM analysis
SEM images of GO and PDA-GO 1:2 with varying resolutions are given in Fig. 5.The pristine GO surface exhibits a smooth scale-like structure due to the presence of oxygen-containing functional groups, as shown in Figs.5a) and 5b).The folded form of the DA-modi ed GO surface almost vanished, revealing a full lamellar structure, and the GO surface grew rougher due to the deposition of PDA nanoparticles, as illustrated in Figs.5c) and 5d).The results demonstrate that DA binds to GO and partially reduces it, while DA self-polymerizes to form PDA encapsulated on the GO surface.In addition, the EDS energy spectra of GO and PDA-GO 1:2 samples were analyzed.The EDS spectrum of PDA-GO 1:2 in Fig. 6 shows that the N element cannot be observed on the surface of GO, whereas in PDA-GO 1:2 , the N element is uniformly distributed on the surface of GO, indicating the homogeneous encapsulation of GO by PDA.

FT-IR analysis
Figure 7a shows the FT-IR spectra of GO and PDA-GO 1:2 samples, with the characteristic peaks of GO visible at wave numbers of 3180 cm − 1 , 1718 cm − 1 , 1622 cm − 1 , 1365 cm − 1 , 1135 cm − 1 , 1039 cm − 1 , and 856 cm − 1 , which represent the telescopic vibration of -OH in the water molecule adsorbed on the graphite carbon layer, the telescopic vibration of C = O in the carbonyl and C = O in the carboxyl group, C = C in the carbon ring on the graphite layer, bending vibration of the hydroxyl group, -OH in the carboxylic acid, C-O in the epoxy group, and out-of-plane bending vibration of the epoxy group, respectively.The FT-IR spectra of PDA-GO 1:2 are compared with those of pristine GO, and it is found that the C = O peak near 1716 cm − 1 of the PDA-GO 1:2 material is signi cantly reduced under the reducing effect of DA, which is due to the partial reduction and covering effect of PDA on GO during the self-polymerization of PDA.In addition, two new peaks appeared at 1508 cm − 1 and 1378 cm − 1 , representing N-H and C-N stretching vibrations, respectively, whereas the characteristic peaks representing epoxide and hydroxyl groups near 856 cm − 1 , 1039 cm − 1 , and 1135 cm − 1 in the original GO disappeared or decreased.The results indicate the binding of DA with GO.Furthermore, due to the π-π interaction of the benzene ring structure of DA with the backbone of GO, the absorption peak of C = C in the original GO was shifted from 1622 cm − 1 to 1577 cm − 1 , indicating that covalent and noncovalent bonding adsorption occurred before DA and GO.

Raman spectral analysis
The structural features of GO and PDA-GO 1:2 were further investigated using Raman spectroscopy.The results are shown in Fig. 7b, in which GO shows a G band at 1591 cm − 1 and a D band at 1286 cm − 1 , with the G band representing the characteristic peaks resulting from the vibration of the graphene lattice, which is a relatively narrow and sharp peak.The D band is a wide and fuzzy peak, representing the characteristic peak induced by defects, impurities or structural incompleteness in GO.The G band of the PDA-GO 1:2 sample migrated to 1595 cm − 1, and the D band migrated to 1302 cm − 1 .The comparison indicates that the conjugate structure of GO is restored after partial reduction of GO by DA.The intensity ratio of D-band to G-band (ID/IG) can be used to measure the disorder of the structure, and an increase in the ID/IG of PDA-GO 1:2 (1.076) compared with that of GO (0.989) has been found, indicating that the effect of covalent bonding increases the disorder of the GO structure.However, the ID/IG of the two was equivalent.The result implies that DA modi cation does not introduce new defects and that the fundamental structure of graphene lamellae is retained, whereas the rise in ID/IG may be due to the π-π interaction between the DA molecules and the GO structure [41,42].

XRD analysis
The XRD spectra of GO and PDA-GO 1:2 samples are given in Fig. 7c.GO exhibits an extremely sharp peak at 2θ = 10.1°,representing the (001) diffraction peak of the graphite oxide phase, and a (002) diffraction peak near 2θ = 25°, corresponding to the graphite phase.There is a shift in the diffraction peak related to the (001) plane; in the XRD spectra of GO, the shift occurs at 10.1°, but in the spectra of PDA-GO 1:2 , it is observed at 2θ = 8.2°.The layer spacing in GO is calculated to be 8.76 Å, but when GO is modi ed to PDA-GO 1:2 , the value is raised to 10.78 Å.The increase might be explained by the reaction of the epoxy groups of DA with the GO basal plane or the π-π interaction between DA and GO.In addition, the decrease in the intensity of the diffraction peak of (001) indicates that GO was partially reduced by DA.

XPS analysis
Figure 8 shows the XPS analysis results of the elemental compositions and chemical structures of GO and PDA-GO 1:2 .Two distinct peaks representing C 1s and O 1s, respectively, were observed in the XPS full spectrum of GO, whereas a weak signal peak representing N 1s appeared near 400 eV in the full spectrum

Analysis of adsorption energy and charge density difference
The interactions of several kinds of oxygen-containing functional groups on GO with DA are discussed in detail in this section, and Fig. 9 displays trend graphs of adsorption energies corresponding to each structure.Figure 10 depicts the charge density difference (∆ρ) after binding as computed by Eq. ( 2).
In Fig. 10, the yellow hue represents the electron-losing zone, whereas the blue color indicates the electron-gaining region.The preferred arrangement of DA on the surface of graphene lamellae is nearly parallel, which is due to π-π interactions of DA with graphene.The distance between the DA ring-graphene surface is 3.2-3.3Å, which aligns with the bonding distance of noncovalent interactions.These ndings are consistent with the phenomenon of DA adsorption on graphene in previous studies [16].The geometry of DA in this case structure remains unchanged, with the amino group on the side away from the graphene lamellae.
According to the charge density difference map, the abundance of strong π-bonds in the pristine graphene lamellae prevents the transfer of excess charge during the interaction with DA.However, in a awed structure, some charge is transferred from the highly electronegative O or N atoms to the H atoms due to hydrogen bonding.
The presence of hydroxyl groups induced a slight distortion of the graphene surface in the S1 structure, but the parallel arrangement between DA and graphene lamellae was maintained, and the location of the amino group remained essentially unaltered.However, favorable hydrogen bonding interactions were formed at a distance of 1.74 Å between the H atoms of the DA hydroxyl (-OH) and the O atoms of the GO hydroxyl group (-OH), which was the main reason for the increase in the adsorption energy of the S1 structure (-1.329 eV) compared to that of the pristine graphene (-1.025 eV) of S0 alkene con guration.
The presence of the epoxy group in the S2 structure causes signi cant deformation of the graphene basal plane, and the amino group is angled in the direction of the graphene lamellae.The presence of the epoxy group causes the departure of DA from the parallel alignment with graphene lamellae, disrupting the initial π-π interactions and preventing hydrogen bonding, further resulting in lower adsorption energy than that of pure graphene (only − 0.805 eV).To evaluate the in uence of the presence of the epoxy group on the adsorption of DA by the hydroxyl group, the hydroxyl group was introduced to the adjacent and para position of the epoxy group to prepare structures S3 and S4, respectively.
A comparison of the two structures and charge density difference plots demonstrate that in S3, DA and graphene akes are not aligned parallel.However, because of hydrogen bonding interactions between the hydroxyl group and the DA, the DA shifts to the side far away from the epoxy group, and the hydroxyl and graphene fragments align almost parallel near the epoxy group, promoting π-π interactions.This results in substantially higher adsorption energy (-1.203 eV) than the S2 structure.The con guration of S4 is similar to that of S3, but the adsorption energy of S4 is -1.388 eV.The reason for the higher adsorption energy of S4 than S3 may be that the epoxy group has a limited effect on the para-hydroxyl group of S4, making the DA con guration in S4 more likely to align parallel with the graphene sheet around the epoxy group.In addition, in this paper, the amino and hydroxyl groups of DA were placed at the edge of GO lamellae, and the structures S5-S8 and S5n-S8n were established by varying the position of the amino and hydroxyl groups of DA relative to the functional groups on GO to investigate the in uence of arrangement on the adsorption of DA at the GO edge.After comparing the structures involving hydroxyl/carboxylic groups on the edges (S5-S7, S5n-S7n) and DA in terms of the con guration and charge density difference, it was found that the amino and hydroxyl groups of DA can create O-H and N-H type hydrogen bonds with hydroxyl/carboxyl groups on GO.However, because π-π interactions are associated with high energy relative to hydrogen bonding, DA molecules will move away from the GO edge along the direction parallel to the graphene sheet throughout the optimization process, which contributes to adsorption energy exceeding that of S0.
The hydroxyl and carboxyl groups in the structures S5 and S6 are in a plane with GO, resulting in a lack of hydrogen bond contact between DA and GO, instead, π-π interactions are maintained.In addition, hydrogen bonding deforms the amino groups in S5n-S7n.The DA molecule changed its initial form and tended to align itself in a single horizontal plane.In S8 and S8n, where carbonyl groups are located at the edges, DA also tends to align with graphene sheets in a parallel manner during the optimization process.
The carbonyl groups at the edges of GO do not form hydrogen bonds with the hydroxyl groups of DA; instead, π-π interactions are maintained.A comparison of the adsorption energies reveals that the values for these con gurations are not signi cantly different from that of structure S0.
The structures, adsorption energies, and charge density difference plots of S1, S9-S12 were investigated to further elucidate how the number of hydroxyl groups on graphene in uences the interaction between DA and GO.It was found that the adsorption energies of DA rise with the increase in the number of hydroxyl groups in the structures S1, S9, and S12 (-1.203 eV, -1.420 eV, and − 1.786 eV).As the number of hydrogen bonds increases, the π-π interactions of DA with graphene lamellae are maintained.In contrast, in S11 and S12, as the number of hydroxyl groups increases, a larger number of oxygen atoms causes serious tilting of DA, and the π-π interactions are destroyed, resulting in lower adsorption energies (only − 1.111 eV, -1.114 eV).
In summary, due to the presence of various types of oxygen-containing functional groups on GO, a portion of DA will enter the GO interlayers via hydrogen bonding or π-π interactions during adsorption, further increasing the interlayer spacing of GO.This nding is consistent with the expansion of the interlayer spacing of the PDA-GO composites in the experimental XRD characterization (Fig. 7c).The presence of the epoxy group in uences the interaction between DA and graphene lamellae but has little impact on the adsorption of its surrounding hydroxyl groups and DA.The sparing inclusion of hydroxyl groups on the graphene sheet, on the other hand, can improve the adsorption capacity of GO on DA by enhancing hydrogen bonding while leaving the π-π connections between DA and graphene intact.When hydroxyl, carboxyl, and carbonyl groups are present at the edges of graphene, their effects on the graphene substrate are negligible.However, when the number of oxygen-containing functional groups on the substrate surface is kept constant, strategically introducing hydroxyl, carboxyl, and carbonyl groups to the edges can further enhance DA adsorption on GO.

Reaction barrier
The TS transition state searching method [36] was used to optimize the calculations to search for the structures of the reactant, transition state, and product.The authenticity and reliability of the reactant, transition state, and product were veri ed by intrinsic reaction coordinate (IRC) scan analysis [37,43].The structure and energy of each reactant, product, and transition state were calculated using DFT, as well as the reaction barrier diagrams for processes and .According to Fig. 11, the amidation of the amino group with the carboxyl group requires 3.96 eV of energy, whereas the ring-opening reaction to the epoxide group demands only 0.71 eV of energy, indicating a smaller potential barrier in reaction and a faster reaction rate, which makes the binding preference of DA for the epoxide group during the GO reduction process.This is consistent with the elimination of the epoxy group peak in the experimental IR spectra (Fig. 7a) following the binding to DA.

HOMO-LUMO energy gaps
We compared the HOMO-LUMO energy gaps of reactants and products in reactions and to evidence that DA increases GO conductivity.Despite several studies [14,15] demonstrating that B3LYP is accurate for the HOMO-LUMO energy gaps of particular macromolecules, the pure density functionals are more accurate for HOMO-LUMO predictions [44].In this study, we used the PBE method, which is based on the optimized structure of the B3LYP method, to perform energy calculations and estimate the HOMO-LUMO energy gap.The conductivity of graphene is lower when an epoxy group is present than when a hydroxyl group is present [45], and a new hydroxyl group is formed in the product of reaction .Accordingly, in this paper, the structure that contains only one hydroxyl group resulting from reaction is referred to as rec, and the product of reaction is referred to as pro; the reactant and product of reaction are referred to as rec and pro.The HOMO-LUMO energy gaps are displayed in Fig. 12.It was found that the energy gap of pro is decreased by 0.259 eV compared to rec, showing that the reduction of the GO epoxy group by DA greatly increases the conductivity of GO.The energy gap of pro does not change signi cantly due to the reduction of DA, and it is only reduced by 0.012 eV compared with that of rec, indicating that the reduction of the carboxyl group by DA does not signi cantly improve the conductivity of GO.

Conclusions
In this study, we prepared PDA-GOn composites with various additive ratios using a straightforward and eco-friendly approach.We employed cyclic voltammetry to analyze the PDA-GOn samples, revealing that PDA-GO 1:2 exhibited superior electrical conductivity, reversibility, and reduced polarization.Additionally, we explored the interaction between graphene oxide (GO) and dopamine (DA) through SEM, XRD, Raman, XPS, and DFT calculations.This investigation encompassed covalent bonding and the impact of the type and quantity of oxygen-containing functional groups on GO concerning DA adsorption.
Our ndings indicated that the coupling of DA with GO led to a signi cant reduction in the number of epoxides, an increase in surface integrity, and a roughly 2 Å expansion in GO layer spacing.This phenomenon could be attributed to the π-π interaction between DA and GO or the covalent binding of DA with epoxides.DFT calculations validated these results, the reaction barrier and HOMO-LUMO energy gaps demonstrate that DA preferentially binds to the epoxy group during the binding process, and the structure's conductivity improved following the reaction.
Further analysis of various structural models revealed that regardless of the initial position of DA relative to GO, DA tended to orient parallel to the GO lamellae during the optimization process.This observation suggests that a portion of DA in ltrates the GO interlayer, forming π-π and hydrogen bonding interactions during the preparation process, thus increasing the interlayer spacing of GO.Defects in GO were also found to impact the interaction, with surface hydroxyl groups increasing the adsorption energy by forming hydrogen bonds with DA.In contrast, the epoxide group signi cantly disrupted the π-π interaction and reduced adsorption energy, although it had minimal in uence on the ortho-hydroxyl group's interaction with DA.Hydroxyl and carboxyl groups near the edge of GO enhanced DA adsorption, while the carbonyl group had no discernible effect.
Remarkably, we observed that the adsorption capacity of GO and DA correlated with the density of functional groups on GO.Speci cally, the enhancing effect of hydroxyl on the GO surface on DA adsorption energy diminished signi cantly after reaching a certain density, such as the presence of 4 hydroxyl groups on 3 carbon rings.This was due to the disruption of the π-π interaction.
In summary, our study provides both experimental and theoretical insights into the interaction between DA-modi ed GO and the mechanism underlying the improvement in GO's electrical conductivity by DA.These ndings offer valuable theoretical guidance for the application of DA-functionalized GO as electrode materials in ow batteries.

Declarations Figures
Schematic illustration for the synthesis of PDA-GOn.
Page 19/28   The CV of GO and PDA-GOn.
The FT-IR (a), Raman (b) and XRD (c) spectra of GO and PDA-GO 1:2 .
The XPS spectra of GO (a) and PDA-GO 1:2 (b). the full spectrum of GO and PDA-GO 1:2 ; the high-resolution C 1 s of GO (c) and PDA-GO 1:2 (d).
Page 25/28 The Variation trend of adsorption energy of S0-S12.
Page 26/28 The side-view of charge density differences between S0-S12.The yellow and light blue regions represent the electron accumulation and depletion.
Reaction barrier diagrams for reactions and .

of PDA-GO 1 : 2 .
The tting analysis of the C 1s energy spectrum of GO revealed four types of peaks, namely, the O-C = O peak at 286.1 eV representing the carboxyl group, the C = O peak at 287.6 eV corresponding to the carbonyl group, the C-O and the C-O-C peaks attributed to the hydroxyl and epoxide groups at 286.6 eV, and the C-C peak at 284.5 eV associated with the carbocyclic group.In contrast, in the C 1s tting pro le of PDA-GO, the peak of the C = O bond is slightly displaced to 287.7 eV, re ecting the presence of the N-C = O bond, while a new peak representing the C-N bond arises at 285.1 eV.The presence of the N-C = O and C-N bonds evidences the binding or encapsulation of DA on the surface of GO.Table3shows the elemental compositions of GO and PDA-GO 1:2 samples.The reduction in the ratio of C-O and C-O-C bonds relative to the C-C bond when DA binds to GO signi es that the epoxy group was consumed during the binding process with the amino group.The occurrence of the peak corresponding to the N-C = O bond and the modest reduction in the O-C = O bond suggest that the carboxyl group was also consumed during the binding process with the amino group, albeit to a smaller extent.These observations show that the DA amino group has been linked to the oxygen-containing functional group on the surface of GO.

Figure 2 GO
Figure 2

Figure 5 GO
Figure 5
the increase of the DA/GO ratio.As shown in Table2, the △Ip of the PDA-GO 1:2 sample has a high potential of 4.146 10 − 3 A, suggesting that the most substantial increase of GO conductivity is obtained at this ratio, and the peak current ratio is at a low level of 1.459, indicating good reversibility.

Table 2
The CV parameter of GO and PDA-GOn.

Table 3
The elemental compositions, O/C ratio, and chemical bonding ratio of GO and PDA-GO 1:2 .