Electrical and Capacitive Response of Hydrogel Solid-Like Electrolytes for Supercapacitors

Flexible hydrogels are attracting significant interest as solid-like electrolytes for energy storage devices, especially for supercapacitors, because of their lightweight and anti-deformation features. Here, we present a comparative study of four ionic conductive hydrogels derived from biopolymers and doped with 0.1 M NaCl. More specifically, such hydrogels are constituted by κ-carrageenan (κC), carboxymethyl cellulose (CMC), poly-γ-glutamic acid (PGGA) or a phenylalanine-containing polyesteramide (PEA). After examining the morphology and the swelling ratio of the four hydrogels, which varies between 483% and 2356%, their electrical and capacitive behaviors were examined using electrochemical impedance spectroscopy. Measurements were conducted on devices where a hydrogel film was sandwiched between two identical poly(3,4-ethylenedioxythiophene) electrodes. The bulk conductivity of the prepared doped hydrogels is 76, 48, 36 and 34 mS/cm for PEA, PGGA, κC and CMC, respectively. Overall, the polyesteramide hydrogel exhibits the most adequate properties (i.e., low electrical resistance and high capacitance) to be used as semi-solid electrolyte for supercapacitors, which has been attributed to its distinctive structure based on the homogeneous and abundant distribution of both micro- and nanopores. Indeed, the morphology of the polyestermide hydrogel reduces the hydrogel resistance, enhances the transport of ions, and results in a better interfacial contact between the electrodes and solid electrolyte. The correlation between the supercapacitor performance and the hydrogel porous morphology is presented as an important design feature for the next generation of light and flexible energy storage devices for wearable electronics.


Introduction
In the last decade, organic electronics has been considered as a key technology for portable and wearable energy-storage devices, such as batteries and supercapacitors, that require flexibility, and lightweight and anti-deformation properties [1][2][3][4][5]. Although batteries can store a high amount of specific energy, they exhibit low power-handling capabilities, delivering electricity at low current densities [6,7]. Instead, supercapacitors provide high specific power and efficiency, as well as a higher cyclic durability than batteries [8,9].
In recent years, progress in the development of flexible supercapacitors has been mainly focused on the manufacture of flexible electrodes, which include not only flexible substrates coated with a thin layer of electrochemically active materials, [10,11] but also free-standing conducting carbon based materials, such as carbon nanotubes-and

Synthesis
The synthesis of the four studied hydrogels has already been reported [28,[34][35][36] and, therefore, a brief description of the employed procedures is only provided.

κ-Carrageenan (κC) Hydrogel
κC has one ester sulfate group in the repeating unit, which forms strong and rigid gels in the presence of K + . In this work, κC was dissolved in water at 2% w/v at ca. 75-80 • C. Then, the corresponding volume of 1 M KCl (10% v/v) was added, and the solution stirred vigorously. Finally, the hydrogel was obtained by cooling the hot κC aqueous solution to room temperature for several hours, enabling a 3D network in which polymeric segments form junction points cross-linked by K + [34]. The κC hydrogel was washed with distilled water three times.

Carboxymethyl Cellulose Sodium Salt (CMC) Hydrogel
CMC (10% wt.) was mixed with water using, firstly, a high speeded magnet mixer and later, as the viscosity increased, manually with a glass rod. Then, the resulting CMC paste was processed in small pieces with a hydraulic press (10 Pa, 1 min), which were kept at 4 • C prior to the formation of the hydrogel. CMC polymeric chains were cross-linked by immersing the pieces into 1.5 M citric acid solution for 24 h at room temperature under slight shaking (80 rpm). [35] The excess of citric acid was removed by washing the pieces four times with distilled water.

Poly-γ-Glutamic Acid (PGGA) Hydrogel
PGGA hydrogel (1 mL) was prepared by dissolving PGGA and EDC in 750 µL of sodium hydrogen carbonate solution (0.5 M) at 4 • C under magnetic stirring. Then, cystamine dihydrochloride, previously dissolved in 0.25 mL sodium hydrogen carbonate solution (0.5 M), was added to the solution and mixed for 2-3 min. The PGGA/EDC/cystamine molar ratio was 5/5/2.5. The final solution was mixed with a magnetic stirrer, and then poured into glass molds. The solution was let to gel at room temperature for one hour [36]. In order to remove any compound in excess, the resulting hydrogel was washed with distilled water three times.

Polyesteramide (PEA) Hydrogel
The synthesis of the di-p-toluenesulfonic acid salt of L-phenylalanine butene 1,4diester and di-p-nitrophenyl fumarate monomers, as well as their polycondensation to produce UPEA chains with C=C double bonds in the backbone, were conducted using the procedure described by Katsarava and co-workers [37]. Functionalized polyethylene glycol, which was used as crosslinker, was prepared using triethylamine and acryloil chloride, as reported in recent work [28]. Then, a 1:4 UPEA:crosslinker (w/w) mixture was dissolved in dimethylacetamide for the reticulation reaction, which was conducted by adding the photoinitiator irgacure 2959 (5% wt.) and exposing the solution to an UV lamp (230 V, 0.8 A) for 4 h at room temperature. The resulting hydrogel was washed with distilled water, which was periodically replaced for 3 days.

Characterization
Infrared absorption spectra were recorded with a Fourier Transform FTIR 4100 Jasco spectrometer equipped with a Specac Model MKII Golden Gate attenuated total reflection (ATR) cell and a heated Diamond ATR. Scanning electron microscopy (SEM) studies were performed using a Focused Ion Beam Zeiss Neon40 scanning electron microscope equipped with an energy dispersive X-ray (EDX) spectroscopy system and operating at 5 kV. Prior to SEM observation, samples were lyophilized. All samples were sputter-coated with a thin carbon layer using a K950X Turbo Evaporator to prevent electron charging problems. Pore size was determined from the SEM images using the software SmartTIFF (v1.0.1.2.).
The swelling ratio (SR, %) of the prepared hydrogels was determined according to where w W is the weight of the hydrogels as prepared (after the washing step) and w D is the weight of the hydrogel after freeze-drying (dried hydrogel). Electrochemical impedance spectroscopy (EIS) diagrams were taken at open circuit (OCP) over the frequency range of 100 kHz to 10 Hz with potential amplitude of 0.05 V using an AUTOLAB-302N potentiostat/galvanostat. All experiments were performed at room temperature using a hydrogel as solid electrolyte sandwiched between two poly(3,4ethylenedioythiophene) (PEDOT) electrodes.
PEDOT electrodes were prepared by chronoamperometry (CA) using a constant potential of 1.40 V under nitrogen atmosphere and at room temperature. A three-electrode one-compartment cell was filled with 50 mL of acetonitrile containing EDOT monomer (10 mM) and LiClO 4 (0.1 M) as supporting electrolyte. Stainless Steel AISI 316 sheets with an area of 6 cm 2 were employed as working and counter electrodes. The reference electrode was an Ag|AgCl electrode containing a KCl saturated aqueous solution (E 0 = 0.222 V vs. standard hydrogen electrode at 25 • C). The polymerization time (θ) was adjusted to obtain PEDOT electrodes with a polymerization charge of 2.67 C (445 mC/cm 2 ).
After data collection, EIS results were then processed and fitted to an electrical equivalent circuit (EEC). The percentage error associated with each circuit element was acceptably low (see next section).

Results and Discussion
The successful preparation of the κC, CMC, PGGA and PEA hydrogels was confirmed by FTIR. The chemical structures derived from the recorded spectra (not shown) were fully consistent with those reported in previous works [22,23,27,29]. From a mechanical point of view, all four systems were flexible and deformable, displaying excellent stability and robustness to keep the electrodes at their positions. Before running EIS analyses, the morphology ( Figure 1) and SR (Equation (1), Table 1) of the four hydrogels were examined.
SEM characterization was conducted to determine the morphology of the hydrogel networks and understand the correlation between pore size and the supercapacitor performance. Representative low and high magnification SEM micrographs of the four studied hydrogels are shown in Figure 1. In spite of their morphological differences, pores can be easily identified in the low magnification micrographs of all samples. Although κC, CMC and PGGA hydrogels present well defined pores with average size of 26 ± 9, 52 ± 14 and 19 ± 8 µm, respectively, the structure of κC is clearly less open than those of CMC and PGGA. Thus, the latter hydrogels show micropores similar to those typically found in honey-comb structures, whereas κC exhibits more compact and less interconnected microporous. In addition to such micrometric pores, representative high magnification micrographs reveal the existence of regions with nanometric pores, which are heterogeneously distributed and are expected to participate in the ion diffusion process. On the other hand, although PEA hydrogel exhibits a more compact structure, micrometric pores with an average size 14 ± 10 µm are clearly identified. Another remarkable difference between PEA and the other three hydrogels is the existence of nanometric pores (534 ± 118 nm) homogeneously distributed throughout the whole surface, which is evidenced in the high resolution SEM micrograph. Therefore, both κC and PEA hydrogels display a more densely SEM characterization was conducted to determine the morphology of the hydrogel networks and understand the correlation between pore size and the supercapacitor performance. Representative low and high magnification SEM micrographs of the four studied hydrogels are shown in Figure 1. In spite of their morphological differences, pores can be easily identified in the low magnification micrographs of all samples. Although κC, CMC and PGGA hydrogels present well defined pores with average size of 26 ± 9, 52 ± 14 and 19 ± 8 µm, respectively, the structure of κC is clearly less open than those of CMC and Swelling measurements gave us additional information about the porous structure of the hydrogels. Indeed, high SR values indicate that the swellable hydrogels are able to hold large amounts of water. In general, the amount of swelling depends on several factors, such as chemical structure, composition, crosslinking density, solvent, among others. Hence, although a porous structure was observed for the four systems, the different natures of the hydrogels could influence the swelling response. The SR of the four studied hydrogels varies as follows: PGGA < κC << PEA << CMC. It is worth noting that CMC shows the largest micropores (Table 1), which explains the very high SR of this hydrogel (SR = 2356 ± 240%). Instead, the average size of the micropores in PEA is comparable to that of PGGA, its high SR (SR = 1416 ± 300%) being attributed to the homogeneous and abundant distribution of nanopores on the whole surface. EIS was employed to investigate the electrical and capacitive performance of κC, CMC, PGGA and PEA hydrogels, which were previously doped by soaking them in 0.1 M NaCl solution prepared with distilled water for 24 h. Then, hydrogels were cut in square cuboids of dimensions 0.5 × 0.5 × 0.1 cm 3 . EIS measurements were conducted at room temperature using a sandwiched configuration, in which each hydrogel piece was arranged separating two PEDOT electrodes at a distance of 0.1 cm ( Figure 2). PEDOT electrodes were prepared as described in the Methods section. PGGA. Thus, the latter hydrogels show micropores similar to those typically found in honey-comb structures, whereas κC exhibits more compact and less interconnected microporous. In addition to such micrometric pores, representative high magnification micrographs reveal the existence of regions with nanometric pores, which are heterogeneously distributed and are expected to participate in the ion diffusion process. On the other hand, although PEA hydrogel exhibits a more compact structure, micrometric pores with an average size 14 ± 10 µm are clearly identified. Another remarkable difference between PEA and the other three hydrogels is the existence of nanometric pores (534 ± 118 nm) homogeneously distributed throughout the whole surface, which is evidenced in the high resolution SEM micrograph. Therefore, both κC and PEA hydrogels display a more densely packed network, which is expected to affect the conductive and capacitive features of the resulting device.
Swelling measurements gave us additional information about the porous structure of the hydrogels. Indeed, high SR values indicate that the swellable hydrogels are able to hold large amounts of water. In general, the amount of swelling depends on several factors, such as chemical structure, composition, crosslinking density, solvent, among others. Hence, although a porous structure was observed for the four systems, the different natures of the hydrogels could influence the swelling response. The SR of the four studied hydrogels varies as follows: PGGA < κC << PEA << CMC. It is worth noting that CMC shows the largest micropores (Table 1), which explains the very high SR of this hydrogel (SR = 2356 ± 240%). Instead, the average size of the micropores in PEA is comparable to that of PGGA, its high SR (SR = 1416 ± 300%) being attributed to the homogeneous and abundant distribution of nanopores on the whole surface.
EIS was employed to investigate the electrical and capacitive performance of κC, CMC, PGGA and PEA hydrogels, which were previously doped by soaking them in 0.1 M NaCl solution prepared with distilled water for 24 h. Then, hydrogels were cut in square cuboids of dimensions 0.5 × 0.5 × 0.1 cm 3 . EIS measurements were conducted at room temperature using a sandwiched configuration, in which each hydrogel piece was arranged separating two PEDOT electrodes at a distance of 0.1 cm (Figure 2). PEDOT electrodes were prepared as described in the Methods section.  The Nyquist and Bode plots, as well as the electric equivalent circuit (EEC) derived from such diagrams, are displayed in Figures 3-6. The quality of the experimental data fitted to the EEC was evaluated to estimate the percentage error associated with each circuit element, being comprised between 0.1% and 6.2% for κC, 0.3% and 7.1% for CMC, 0.3% and 5.2% for PGGA, and 0.3% and 5.1% for PEA. The EEC obtained for CMC, PGGA and PEA are identical (Figures 4-6), while κC exhibits a more complex ECC with two additional elements ( Figure 3). The Nyquist and Bode plots, as well as the electric equivalent circuit (EEC) derived from such diagrams, are displayed in Figures 3-6. The quality of the experimental data fitted to the EEC was evaluated to estimate the percentage error associated with each circuit element, being comprised between 0.1% and 6.2% for κC, 0.3% and 7.1% for CMC, 0.3% and 5.2% for PGGA, and 0.3% and 5.1% for PEA. The EEC obtained for CMC, PGGA and PEA are identical (Figures 4-6), while κC exhibits a more complex ECC with two additional elements (Figure 3).   The measured Nyquist plots, in which the real part of the impedance (Z) is plotted against the imaginary part (Z'), show a semicircle in all cases. The starting point of each curve (i.e., the intercept of the curve with the real Z-axis in the high frequency region) indicates the electrolyte resistance (RS), [38] that is, the resistance of the doping solution inside the hydrogel pore. RS only depends on the ionic concentration, type of ions, temperature and the geometry of the area in which the current is carried (i.e., hydrogel mesh size). Considering that in this work all hydrogels were soaked in a 0.1 M NaCl electrolytic solution and that the temperature was very similar in all experiments, the small variation expected among the different analyzed systems should be attributed to the different concentration of NaCl inside the hydrogels (i.e., the doping capacity of the hydrogels) and the morphology of the hydrogel (i.e., mesh size), which may lead to a nonuniform ion concentration in the electrolyte. Thus, the lower the concentration and the ion mobility (i.e., more restricted by the morphology) in the hydrogel, the higher the RS value will be.
Although the RS values displayed in Figures 3-6 are of the same order of magnitude, they increase as follows: PEA (3.11 Ω) < PGGA (5.92 Ω) < CMC (6.27 Ω) < κC (8.18 Ω). κC exhibited the most compact structure (Figure 1a) and, therefore, the largest area, which The measured Nyquist plots, in which the real part of the impedance (Z) is plotted against the imaginary part (Z'), show a semicircle in all cases. The starting point of each curve (i.e., the intercept of the curve with the real Z-axis in the high frequency region) indicates the electrolyte resistance (R S ), [38] that is, the resistance of the doping solution inside the hydrogel pore. R S only depends on the ionic concentration, type of ions, temperature and the geometry of the area in which the current is carried (i.e., hydrogel mesh size). Considering that in this work all hydrogels were soaked in a 0.1 M NaCl electrolytic solution and that the temperature was very similar in all experiments, the small variation expected among the different analyzed systems should be attributed to the different concentration of NaCl inside the hydrogels (i.e., the doping capacity of the hydrogels) and the morphology of the hydrogel (i.e., mesh size), which may lead to a nonuniform ion concentration in the electrolyte. Thus, the lower the concentration and the ion mobility (i.e., more restricted by the morphology) in the hydrogel, the higher the R S value will be.
Although the R S values displayed in Figures 3-6 are of the same order of magnitude, they increase as follows: PEA (3.11 Ω) < PGGA (5.92 Ω) < CMC (6.27 Ω) < κC (8.18 Ω). κC exhibited the most compact structure (Figure 1a) and, therefore, the largest area, which affected negatively the entrance of ions. Both CMC and PGGA exhibit pseudo-honeycomb structures with very similar R S values, which are intermediate between those of κC and PEA. Finally, the low R S value obtained for PEA is ascribed to its different microstructure: open interconnected pores surrounded by regions with compact morphology and homogeneously distributed throughout the surface following a bimodal distribution (Figure 1d). This feature, which resembles that proposed by Wang et al. at low temperature, [39] in addition to other factors, such as tortuosity, dead-end pores or the orientation of the microstructure, [40] might affect ion mobility inside the hydrogel. Overall, the resistivity of the doped hydrogel increases with R S . Thus, when the solution resistance increases, this means that the resistivity of the electrolyte solution increases and the pore area (solid phase area) decreases. geneously distributed throughout the surface following a bimodal distribution ( Figure  1d). This feature, which resembles that proposed by Wang et al. at low temperature, [39] in addition to other factors, such as tortuosity, dead-end pores or the orientation of the microstructure, [40] might affect ion mobility inside the hydrogel. Overall, the resistivity of the doped hydrogel increases with RS. Thus, when the solution resistance increases, this means that the resistivity of the electrolyte solution increases and the pore area (solid phase area) decreases. The diameter of the semicircle corresponds to the charge transfer resistance (RP) at the PEDOT electrode/hydrogel interface, also known as the interface reaction resistance [38]. Specifically, this element accounts for the ionic resistance (electrolyte resistance in the porous structure of the electrolyte) and the electronic resistance, which comprises the The diameter of the semicircle corresponds to the charge transfer resistance (R P ) at the PEDOT electrode/hydrogel interface, also known as the interface reaction resistance [38]. Specifically, this element accounts for the ionic resistance (electrolyte resistance in the porous structure of the electrolyte) and the electronic resistance, which comprises the intrinsic resistance of the electrode material and the contact resistance between the active layer and the current collector. In all cases, the R P , which includes the resistance of the hydrogel and the PEDOT electrodes, is slightly lower than the R S . The values R P obtained for κC, PGGA and PEA are similar (i.e., 2.89, 2.49 and 2.17 Ω, respectively) and lower than that of CMC (5.57 Ω), which indicates that the former hydrogels present better interfacial contact between the electrodes and the solid-like electrolyte. Indeed, the better the interfacial contact, the faster the ion transport and the lower the interfacial resistance.
The Bode diagrams, which represent the frequency response of impedance (Figures 3b  and 6b) and phase angle (Figures 3c and 6c), display two time constants. The first is below 10 1 Hz and is related to the hydrogel, whereas the second is around 10 3.2 , 10 3.6 , 10 3.9 and 10 4.0 Hz for κC, CMC, PGGA and PEA hydrogels, respectively. The second time constant has been associated with the interface between the PEDOT electrode and the hydrogel.
intrinsic resistance of the electrode material and the contact resistance between the active layer and the current collector. In all cases, the RP, which includes the resistance of the hydrogel and the PEDOT electrodes, is slightly lower than the RS. The values RP obtained for κC, PGGA and PEA are similar (i.e., 2.89, 2.49 and 2.17 Ω, respectively) and lower than that of CMC (5.57 Ω), which indicates that the former hydrogels present better interfacial contact between the electrodes and the solid-like electrolyte. Indeed, the better the interfacial contact, the faster the ion transport and the lower the interfacial resistance. The Bode diagrams, which represent the frequency response of impedance (Figures 3b  and 6b) and phase angle (Figures 3c and 6c), display two time constants. The first is below 10 1 Hz and is related to the hydrogel, whereas the second is around 10 3.2 , 10 3.6 , 10 3.9 and 10 4.0 Hz for κC, CMC, PGGA and PEA hydrogels, respectively. The second time constant has been associated with the interface between the PEDOT electrode and the hydrogel.
Based on their definition, the sum of the electrolyte resistance (RS) and the interfacial resistance (RP) can be interpreted as the internal resistance (Rb = RS + RP), which corresponds to the bulk resistance of the whole device [38]. The values of Rb increase as follows: Based on their definition, the sum of the electrolyte resistance (R S ) and the interfacial resistance (R P ) can be interpreted as the internal resistance (R b = R S + R P ), which corresponds to the bulk resistance of the whole device [38]. The values of R b increase as follows: PEA (5.28 Ω) < PGGA (8.41 Ω) < κC (11.07 Ω) < CMC (11.84 Ω). Overall, the conductive properties of the supercapacitor device based on PGGA and, especially, PEA are superior to those of κC and CMC, which we ascribe to their better interfacial contact and the hydrogel structure (Figure 7).
The bulk conductivity (σ) of the prepared doped hydrogels is 76, 48, 36 and 34 mS/cm for PEA, PGGA, κC and CMC, respectively. It is worth noting that the conductivity of these biohydrogels is comparable to those reported for PVA-containing hydrogels; for instance, PVA doped with H 3 PO 4 or H 2 SO 4 (11.6 or 7.1 mS/cm, respectively), [41,42] PVA doped with H 3 PO 4 and 2-mercaptopyridine (22.6 mS/cm), [41] PVA doped with H 2 SO 4 and indigo carmine or alizarin red S (20.3 or 33.1 mS/cm, respectively), [43] chemically crosslinked PVA-poly(ethylene glycol) (67.1 mS/cm) [44] and KCl doped boron crosslinked PVA (38 mS/cm). [45] Moreover, the ionic conductivity of a 0.1 M NaCl aqueous solution is~20 mS/cm, a concentration of 1 M NaCl being required to obtain a value comparable to that of doped PEA hydrogel [46]. This feature evidences the important role of the hydrogel structure in the mobility of ions.
The EEC used to fit the experimental EIS results for CMC, PGGA and PEA corresponds to the Randles-type electrical equivalent circuit [47]. In addition to RS and RP, the diagram shows two additional elements: (1) the capacitance C of the hydrogel in parallel with RP; and (2) the constant phase element (CPE), which is associated with the capacitance of the electrical double layer (Cdl) on the electrode surface, in series with RP. In the case of κC, the CPE is in parallel with resistance and, in addition, it shows a tangent hyperbolic diffusion element (T), also named bounded Warburg, which is common for porous electrodes.
The perfect semicircle obtained in the Nyquist plot for all the studied systems indicates that the four doped hydrogels behave as ideal capacitors. Accordingly, the capacitance C, which is in parallel with RP, reflects their ability to store charge. The C values obtained for κC, CMC, PGGA and PEA are 5.56, 7.72. 9.36 and 10.2 µF, respectively. Thus, the amount of accumulated charge increases with decreasing RS, which evidences that the capacitance improves with the mobility and transport of ionic charge.
The Cdl is associated with the separation of charges at the electrode/electrolyte interface. The double layer capacitance was represented with a CPE, which describes a nonideal capacitor when the phase angle is different from −90°, to model the heterogeneity of the samples. The CPE impedance is attributed to the distributed surface reactivity, surface heterogeneity, and roughness of the current and potential distribution, which in turn are related to the electrode geometry and the electrode porosity [48]. The CPE impedance has been expressed as = [ ( · ) ] The EEC used to fit the experimental EIS results for CMC, PGGA and PEA corresponds to the Randles-type electrical equivalent circuit [47]. In addition to R S and R P , the diagram shows two additional elements: (1) the capacitance C of the hydrogel in parallel with R P ; and (2) the constant phase element (CPE), which is associated with the capacitance of the electrical double layer (C dl ) on the electrode surface, in series with R P . In the case of κC, the CPE is in parallel with resistance and, in addition, it shows a tangent hyperbolic diffusion element (T), also named bounded Warburg, which is common for porous electrodes.
The perfect semicircle obtained in the Nyquist plot for all the studied systems indicates that the four doped hydrogels behave as ideal capacitors. Accordingly, the capacitance C, which is in parallel with R P , reflects their ability to store charge. The C values obtained for κC, CMC, PGGA and PEA are 5.56, 7.72. 9.36 and 10.2 µF, respectively. Thus, the amount of accumulated charge increases with decreasing R S , which evidences that the capacitance improves with the mobility and transport of ionic charge.
The C dl is associated with the separation of charges at the electrode/electrolyte interface. The double layer capacitance was represented with a CPE, which describes a non-ideal capacitor when the phase angle is different from −90 • , to model the heterogeneity of the samples. The CPE impedance is attributed to the distributed surface reactivity, surface heterogeneity, and roughness of the current and potential distribution, which in turn are related to the electrode geometry and the electrode porosity [48]. The CPE impedance has been expressed as where Y 0 is the admittance of an ideal capacitance and n is an empirical constant, ranging from 0 to 1. When n = 1, the CPE behaves as a pure capacitor and Y 0 = 1/C, while the CPE behaves a pure resistor and Y 0 = 1/R when n = 0. Furthermore, when n = 0.5, the CPE is associated with a diffusion process, being the equivalent of the so-called Warburg element (W) and Y 0 = √ 2/W. The n values obtained for κC and PEA (n = 0.845 and 0.807, respectively) are close to 1, while those of CMC and PGGA (n = 0.362 and 0.646, respectively) are close to 0.5.
The T diffusion element found in the EEC of κC, which is characteristic of films that contain a fixed amount of electroactive material, [49,50] in this case PEDOT, appears when the electroactive material cannot be replenished once it has been consumed. The T element is characterized by two parameters, an "admittance" parameter, Y 0 , and a time constant parameter, B (units: sec 1 2 ): The parameter Y 0 is related to the diffusion coefficient for the mobile species within the film. In this case, the T element has been associated with the counter ions confined into the PEDOT film situated between the metal substrate and the κC solid electrolyte. This confinement, which may be due to the compact structure of the hydrogel, is also responsible for the apparition of a resistance element linked to the electrode.
Hydrogels based on biopolymer-derived networks have emerged as a green energy approach to produce solid-like electrolytes. The four polymeric systems studied, which have been successfully applied as supercapacitors, are presented as technology options for energy storage devices. From a fundamental aspect, the characterization by EIS of the ionic and capacitive properties allowed us to choose the most suitable option. Most importantly, the correlation between such performance and the hydrogel porous morphology can be used as a design tool for the next-generation innovative systems.

Conclusions
In summary, the doped polyesteramide hydrogel, which displays micropores, as well as nanometric pores, homogeneously distributed throughout the whole surface, presents better properties as a solid-like electrolyte than doped biohydrogels with pseudohoneycomb and compact heterogeneous structures. Indeed, the polyesteramide hydrogel shows a low electrical resistance, a high capacitance and good interfacial contact with the electrode, thus meeting the electrical requirements of solid-like electrolytes for supercapacitors. The full characterization of the hydrogel solid-like electrolytes by EIS provides additional valuable data (i.e., ionic and capacitive properties) to select the most adequate system. In addition, the hydrogel morphology, which has a significant effect on the device performance, is required to be highly porous and open. The correct optimization of these parameters would improve the application of biopolymer-derived hydrogels in light and wearable flexible devices.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.