Ionic conductivity and dielectric properties of bulk SPP-PEG hydrogels as Na+ ion-based SPE materials for energy storage applications

Rudramani Tiwari a, Dipendra Kumar Verma a, Devendra Kumar a, Shashikant Yadav a, Krishna Kumar b and S. Krishnamoorthi *a
aDepartment of Chemistry, Centre of Advanced Studies, Institute of Science, Banaras Hindu University, Varanasi 221005, India. E-mail:; Tel: +91 9450200221
bDepartment of Chemistry and Environmental Science, Madan Mohan Malaviya University of Technology, Gorakhpur -273010, India

Received 8th April 2021 , Accepted 14th June 2021

First published on 15th June 2021


In this work, a green SPP-PEG hydrogel material, containing Na+ ions, was synthesized by a green chemistry method using sodium polyphosphate and polyethylene glycol in water. This hydrogel has an amorphous morphology and a sandwiched matrix with a floating layer, which allows ions to move easily inside the matrix. Flexibility and sticky nature are the key properties that enable forming a good interface on the electrode surface. The hydrogel tends to change to the plasma phase above 70 °C. A Na+ ion–based hydrogel electrolyte shows a stability window of 2.75 volts with >96% ionic nature of conductivity in the order of 10−4 S cm−1 with a diffusivity constant in the order of 10−9 m2 s−1 and mobility in the order of 10−7 m2 V−1 s−1 at room temperature. The hydrogel matrix shows cage-type hopping with a value of power exponent >1 at lower temperatures, and the activation energy of ionic movement was observed to be quite low, i.e. 0.488 eV. Dielectric properties of the hydrogel show a high amount of capacitance with negligible electrode contribution. Regarding temperature dependence, this study confirms that conductivity and matrix relaxation are independent of time and temperature.


Traditional energy storage devices using liquid-state electrolytes are unable to fulfill the requirement of promising portable and wearable electronic devices due to their bulkiness and electrolyte leakage risks.1 Therefore, to solve these problems, it is necessary to develop energy storage systems/devices with fixed-state electrolytes, i.e. semi-solid state and solid-state electrolytes. These electrolytes stabilize the phase property, thereby reducing the risk of electrolyte leakage in device packing.2,3

The hydrogel is an elastic, 3D cross-linked hydrated polymeric matrix with high content of water, which makes them wet and soft giving a gel-like appearance.4 The ionic salts on the polymer chains can efficiently attract and localize ions, due to the presence of a significant amount of trapped water as a solvent inside the matrix. This property of the system preserves the stability of the solid matrix with flexibility.5 The basic problem associated with hydrogel electrolytes is water splitting during electrochemical reactions, oxygen-evolution reactions (OERs) and hydrogen-evolution reaction (HERs), due to the low-stability working potential window of the water molecule.6,7 Another problem is the evaporation of the solvent accompanied by the concentration of the polymer electrolytic salts.8 Both problems are eliminated by using a method to make solvent molecules as part of a polymer or minimize concentration inside the matrix. Polymeric materials are rich in hydrophilic functional groups, which facilitate the formation of abundant intra-molecular or intermolecular H-bonds.9 This endows polymeric hydrogels with specific properties such as stretchability, self-healing ability, and flexibility.10 These materials have gained much interest with the rapid progress of electronic devices because they can maintain their inbuilt electrochemical function under mechanical strain.11

Nowadays, rechargeable Li-ion batteries dominate the market. There are some critical drawbacks present in using Li+ ion batteries, which include low working temperature range, flammable nature, high cost and limited natural abundance.12 These drawbacks made us thoughtful to find their alternatives. Sodium is a promising candidate for substituting the Li metal in electronics due to its good electrochemical properties, high safety, low cost, large natural reserve, environmental friendliness, and Na intercalation chemistry.13 Aqueous rechargeable sodium-ion electrolytes show great potential for application in energy storage devices due to the above-discussed properties.14 Rechargeable aqueous sodium-ion batteries show poor results with inorganic anode materials due to the small electrochemical stability window of water and reaction with anode materials. However, compared to inorganic anodes, organic anodes, i.e. polymeric anodes and NASICONs, are highly capable and applicable anodic materials for the hydrogel system.15 Sodium polyphosphate (SPP) is an inorganic polymeric salt containing a large amount of sodium ions in its functional group. Sodium polyphosphate has great application potential in our daily life activities and is used in food industries, medical industries, ceramics, anti-cracking agents, anti-flaming agents, etc.16,17 SPP is highly capable of holding water in the hydrated form. It was also reported that SPP can be used as an electrode material for sodium-ion batteries.18,19 Polyethylene glycol (PEG) is a low-molecular weight water-soluble organic polymer, which also acts as a plasticizer, solvent, etc., with great application potential in organic electronics.20,21 Both SPP and PEG are eco-friendly, non-toxic and non-flammable materials. These are promising agents for green and safe applications in electronics.

In this study, we prepared a blend of polymeric hydrogels using an inorganic polymer sodium salt, i.e. SPP, and a water-soluble organic polymer, i.e. PEG, by a green chemistry method. A stable film of hydrogel was prepared and characterized by various methods, i.e. IR spectroscopy, XRD, SEM-EDS, TGA-DTA, LSV, CV, voltage sweep, and EI spectroscopy to elaborate its chemical, morphological, thermal, electrochemical, conducting and dielectric properties. Temperature dependence experiments were performed to understand the change in the electrical and dielectric properties of the material with respect to temperature in the range of 20 °C to 80 °C.


Preparation of SSP-PEG hydrogels

First, 1 g of sodium polyphosphate (SPP), 200 × 10−6 L of polyethylene glycol (PEG) 600 and 1.5 mL of distilled water were taken in a test tube and sonicated at 50 °C for 30 min. A clear transparent solution was obtained, which was further dried in an oven at 62–65 °C for 24 hours and 2–3 times rubbed up the gel using a spatula during the drying process. The hydrogel was covered by a tissue paper at room temperature to remove the excess PEG. Finally, 1.20 g of the final product was obtained as a solid hydrogel (SSP-PEG hydrogel).

Result and discussion

Here we successfully prepared an SPP-PEG hydrogel material by a green method, using PEG 600. We also prepared a hydrogel material using PEG 400. We observed that the matrix configuration with PEG 600 is more stable than that with PEG 400 due to its highly viscous nature. The prepared material is non-toxic, non-flammable, non-hazardous, eco-friendly and cheaper. All the materials used for hydrogel preparation are cheaper, non-hazardous and eco-friendly; moreover, the preparation procedure is carried out under normal conditions in an open environment without using any energy and no by-products were formed, indicating the method is economic as regards the energy and atom expenditure. Our material and methodology completely followed the principles of green chemistry. All these parameters refer that the material is a green material and prepared by green chemistry. The molecular formula of SPP can be written as [Na(PO3)]n, which clearly indicates that one monomeric unit of SPP has three oxygen atoms. These oxygen atoms tend to form hydrogen bonds with water molecules, which indicate that SPP has a great tendency to make a hydrated system in a hydrogel matrix. PEG also has oxygen atoms on its backbone, which also participate in hydrogen bonding. In the SPP-PEG hydrogel, water was used as a solvent, which was captured inside the matrix; here some amount of SPP was present in an ionic form inside the matrix but the major part of SPP was present in a hydrated form only because of the low abundance of the solvent molecule inside the matrix. Intermolecular H-bonding is dominating the interaction over the ionic interaction inside the matrix, which is shown in Fig. 1. The intermolecular interaction allows the formation of various layering structures, which are attached with another layer by this force. During heating of the hydrogel, it is observed that when the temperature increases above 40 °C, the hard matrix becomes very flexible and at a temperature above 70 °C, the matrix gets converted from a semi-solid hydrogel into a thin-film plasma-like phase. This confirms that only the outer layer is dehydrated and a thin solid film is formed, and that the inner matrix is a less viscous fluid compared to the hydrogel matrix and slightly free to move and change its shape corresponding to the gravitational force. The formed outer thin solid film prevents inner layers from dehydration and provides a boundary to the inner fluid material, which is unable to move outside of it. Under such conditions, the hydrogel material changes into a plasma material at high temperatures. The prepared hydrogel material is flexible, transparent and sticky in nature. This flexible property of the hydrogel material makes it a perfect candidate for device preparation. The stickiness of the material is a good property to make a better interface with electrodes. Images showing the matrix phase, flexibility, transparency and stickiness are given in Fig. 1.
image file: d1qm00537e-f1.tif
Fig. 1 Preparation of the SPP-PEG hydrogel matrix with weak interactions between different atoms, and graphical representation of the sandwiched floating layer matrix: (A and B) non-hygroscopic nature confirmed by a dry tissue paper test. (C–E) Flexibility with a twisting property. (F) Steady phase property. (G) Sticky property. (H) Transparent nature of the hydrogel material.

The IR spectrum of the SPP-PEG hydrogel (Fig. 2(A)) shows all characteristic bands for hydrogel formation. A band at 3617 cm−1 is attributed to the free O–H stretching vibration of the water molecule. A broad band was also observed between 3200 and 3600 cm−1 frequency range, which is ascribed to the O–H stretching vibration of the hydrogen bond in water and the alcohol group present in the matrix. The band near 2881 cm−1 is assigned to the C–H stretching vibration of PEG present inside the matrix. The band at 2368 cm−1 is ascribed to the hydrogen-bonded O–H bending vibration of water with the P[double bond, length as m-dash]O⋯H–O bond, and the band at 1780 cm−1 arises for P–O⋯H–O bending. The bands at 1645 cm−1 and 1475 cm−1 are ascribed to the alcoholic O–H bending vibration of PEG and free water O–H def. respectively. Instant bands appear at 1253 cm−1 and 720 cm−1, ascribed to P[double bond, length as m-dash]O stretching and P–O stretching respectively. The characteristic P–O–P stretching band merged with the P–O stretching band at 720 cm−1. The band at 1080 cm−1 is assigned to C–O–C stretching and the band at 862 cm−1 represents C–H detraction of PEG. The merged band at 500 cm−1 represents the P–P bond with P–O–P asymmetric stretching in the matrix.22–24

image file: d1qm00537e-f2.tif
Fig. 2 (A) IR spectrum, (B) TGA (red line) and DTA (blue line) and (C) XRD pattern of the SPP-PEG hydrogel and SPP salt. (D) LSV analysis, (E) CV analysis and (F) current versus time plot of the SPP-PEG hydrogel.

In the TGA-DTA curve (Fig. 2B), up to 115 °C temperature, 4% weight loss is observed for the removal of absorbed moisture from the outer layer of the sample. At 115 °C temperature, the DTA curve (onset) shows an exothermic reaction inside the matrix, which refers to the phase change of the hydrogel matrix to a crystalline matrix and the corresponding temperature said to be crystallization temperature (Tc). Between 133 °C and 150 °C, 7% weight loss is observed in a very sharp manner with endothermic reactions due to the removal of water molecules from the inside of the crystalline matrix. At 215 °C to 230 °C, 3% weight loss observed with absorbing heat refers to the removal of hydrated water molecules from the matrix crystals. At 310 °C to 360 °C temperature, 11% weight loss is observed for PEG chain degradation in the form of CO and CO2. It is confirmed by two-step heat absorption between 310 °C and 330 °C and 330 °C and 360 °C for CO and CO2 respectively. The TGA-DTA curve shows the melting temperature (Tm) of the material to be 630 °C. Below Tc, there is no degradation observed for the hydrogel system, which indicates that the material is thermally stable for use as a hydrogel electrolyte system.25,26

The XRD pattern shows that the intensity of diffraction was suppressed in the SPP-PEG hydrogel diffraction plot compared to the SPP diffraction plot (Fig. 2(C)). It is observed that the band on-set value for SPP diffraction is observed near a theta value of 21°, band mid-set observed at 26° and band end-set at 39°. For SPP-PEG hydrogel bands, on-set, mid-set, and end-set shifted and were observed at 24°, 30°, and 38° respectively. This study confirms a huge change in the molecular arrangement of the hydrogel matrix due to the interaction of water and the PEG molecule with SPP. In both diffraction patterns, broad bands confirm the amorphous nature of the material. The change in the percentage crystalline nature of the SPP-PEG hydrogel with respect to SPP can be calculated by area under the curve values of both matrixes. The percentage crystalline nature can be calculated using the following relation:27

Xcryst = (Ac/At) × 100
where Xcryst is the percentage crystalline nature, Ac the area under the curve, and At the total area of the plot. Since SPP and SPP-PEG hydrogels show 25.45% and 15.68% crystalline nature, they show a decrease of 38.38% in the crystalline nature of the hydrogel matrix.

Linear sweep voltammetry (LSV) analysis shows that current is continuously increasing with the increase in voltage, which indicates that the material is highly electrochemically active. The LSV plot in Fig. 2(D) shows a plateau region in the positive voltage range from 0.32 V to 3.07 V. Before this voltage range, current is suddenly decreased and after this voltage, current is drastically increased due to instability in the corresponding voltage. The observed plateau region refers to an electrochemical stability window (ESW) of 2.75 V for the application of the hydrogel material.28 The CV plots for the SPP-PEG hydrogel (Fig. 2(E)) shows pseudo-rectangle behaviour without an oxidation–reduction band in a voltammogram for the ESW region. The voltammogram also shows that the material has a large amount of charge density due to the capacitive behaviour of the material.29

The total current (It) flow inside the matrix represents the sum of the total ionic current (Iion) and total electronic current (Ie)/residual current (It= Iion+ Ie). The transference number measurement is performed by Wagner's DC polarization method to determine the nature of charge carrier inside the matrix, i.e. ionic or electronic. A characteristic polarization current vs. time plot (Fig. 2F) shows a rapid fall in the initial current (Ii) from its initial value, showing a continuous decrement up to 18[thin space (1/6-em)]000 seconds. We record the final current value (If) at a given time. The total ionic transference number was calculated using the following relation:30

Iion = (IiIf)/Ii
For the hydrogel matrix, the total ionic transference number was found to be >0.96. The ionic transference number study confirms that the maximum charge career species present inside the matrix are ionic in nature.

The surface morphology at a low magnification shows that the film contains a large amount of fluids over the matrix (Fig. 3A). At high resolution, floating layers are found on the fluid surface and these layers are sandwiched between each other (Fig. 3B); it was also observed that some small blocks with a size <2 microns are floating on the fluid layer. Upon further magnification, the surface image shows that there are many interstitial spaces present inside the matrix with a nano-meter scale size (Fig. 3C). Overall morphological information indicates that the matrix of hydrogel contains sandwiched solid and fluid layers with small solid blocks and interspatial spaces, which can endow phase transformation properties under different physical conditions such as temperature, pressure, etc. The EDS study shows that the matrix contains 14.4% w/w (18% theoretically) sodium (Fig. 3E) for selected area (Fig. 3D) of the hydrogel film.

image file: d1qm00537e-f3.tif
Fig. 3 (A–C) SEM image and (D and E) EDS selected area and spectrum of the SPP-PEG hydrogel.

Impedance spectroscopy (IS) is a useful technique for the characterization of the conducting and di-electrical properties of the material.31–38 Thus, the complex impedance formalism of the output response allows direct separation of the bulk material effect, grain boundary effect and electrode interfacial phenomena. Complex impedance spectrograph of materials can be given by the following relation:

Z* = Z′ − iZ′′
where Z* represents the complex impedance, Z′ the real part of the impedance and iZ′′ the imaginary part of the impedance. The semicircular arc of the Nyquist plot is associated with the bulk resistance (Rb) and capacitance of the material. An intercept of the imaginary part on the real part of the impedance gives Rb on the lower frequency side. The bulk conductivity (σbulk)/DC conductivity (σdc) of the material can be determined with Rb using the following relation:
σbulk = (1/Rb)(l/A)
where l is the thickness of the sample and A the area of the sample electrode interface. The Nyquist plot shows a depressed semicircle on the high-frequency side, making an intercept on the real axis with a spike (for a large value of imaginary part) with an inclination less than the right angle in the low-frequency region (Fig. 4A). Rb of the SPP-PEG hydrogel shows nearly 5 kilo Ohm range at 20 °C and bulk conductivity in the range of ∼10−4 S cm−1. In temperature dependence study, it was observed that Rb of the sample gradually decreases with the increase in temperature, and at 80 °C, Rb of the sample shows 200 Ohm (inset of Fig. 4A) and conductivity in the range of ∼10−3 S cm−1. With the increase in temperature, the matrix of the hydrogel material gets relaxed and allows ions to move easily inside the sample, which is responsible for the gradual increment in bulk conductivity.

image file: d1qm00537e-f4.tif
Fig. 4 (A) Cole–Cole plot of the SPP-PEG hydrogel at different temperatures. (B) AC conductivity spectra of the SPP-PEG hydrogel at different temperatures (curves are fitted using relation σ = σo + Afn). (C) Plot of log[thin space (1/6-em)]σdcvs. 1000/T for the SPP-PEG hydrogel material showing Arrhenius-type behaviour. (D) Curve of tan[thin space (1/6-em)]δ vs. f (Hz) for the SPP-PEG hydrogel at different temperatures. (E) Scaled AC conductivity master curve plotted between σac/σdc and f/fH. (F) Scaled loss tangent (tan[thin space (1/6-em)]δ) master curve plotted between tan[thin space (1/6-em)]δ (tan[thin space (1/6-em)]δmax) and f/fmax.

Frequency-dependent conductivity/AC conductivity (σac) spectra (Fig. 4B) consist of three separate regions with the increasing frequency. The first dispersion region arising in the low-frequency region refers to accumulations of free charge carriers near the electrolyte–electrode interface. The middle plateau region is related to the frequency-independent conductivity (σbulk/σdc) of the sample material. Again at a high frequency, another dispersion region is observed, in which σac suddenly increases with the increase in frequency. This region is observed due to the capacitive behaviour of the material (capacitive reactance, Xc = 1/2πf). For making a proper understanding of the transport mechanism of charge carriers and their ion dynamics, AC conductivity analysis of amorphous/solid electrolyte systems is a very useful parameter. This AC conductivity spectrum for the SPP-PEG hydrogel follows Jonscher's power law (JPL), which is given as follows:

σac = σdc + Afn
where σdc is the DC conductivity, A is a constant (pre-exponential frequency factor/dispersion parameter), and n is the power exponent. This equation was used to fit the AC conductivity data as a non-linear curve fitting function. The AC conductivity spectra of these samples at different temperatures follow JPL and the value of power exponent ‘n’ lies in the range of 0.33 to 1.16. For the SPP-PEG hydrogel system, the value of ‘n’ indicates two different types of hopping, i.e. caged type (n > 1) at a lower temperature (<40 °C) due to the rigid packing of the hydrogel system, so that the Na+ ion never gets the support of the segmental motion of polymer chains. The second hopping is a correlated type (n < 1) at a high temperature (>40 °C) due to the change in the phase of the matrix and more flexible packing of the hydrogel system, so that the charge carriers hop from one interface to another, which is supported by the segmental motion of polymer chains.

The pre-exponential frequency factor/dispersion parameter (A) and power exponent ‘n’ values are varied simultaneously to acquire best fits. R2 shows the parameter for fitting goodness, and it was found that at all temperatures, the value of R2 is >0.97, indicating that the goodness of the fitting was satisfactory. When we extrapolate the plateau region of the plot on the y-axis, it gives the values of DC conductivity for the sample at all temperatures. It was observed that the value of DC conductivity calculated from the Nyquist plot analysis and DC conductivity obtained by extrapolating the plateau region on the y-axis give very closer values. The values of σdc, A, n and R2 for different temperatures are given in Table S1 (ESI).

The dependence of the conductivity on the temperature can be derived from thermally activated voltage fluctuations across the insulating area of the matrix, which modulates the effective conduction barriers. Temperature-reliant σdc of the SPP-PEG hydrogel follows the thermally activated process which is Arrhenius type.

This characteristic of the material is useful to determine the essential minimum amount of energy needed for ions to move from one place to another inside the hydrogel matrix. This is known as the activation energy (Ea) for ionic electrolyte systems. It can be determined using the following relation:

σT = σ0[thin space (1/6-em)]exp − Ea/kT
where σ0 is the pre-exponential factor, Ea the activation energy (eV), k the Boltzmann constant and T the temperature (K). Fig. 4(C) shows the log[thin space (1/6-em)]σdcvs. 1000/T plot for the SPP-PEG hydrogel, which shows Arrhenius-type thermal activation behaviour, and the value of activation energy (Ea) calculated is 0.488 eV. It is possible to scale AC conductivity spectra into a single master curve for the material with different compositions at different temperatures.39 The frequency axis of the master curve is scaled by hopping frequency fH. In the AC conductivity plot, the frequency parallel to the onset of conductivity dispersion is recognized as the hopping frequency. At an fH value of σac = 2σdc, this relation is helpful to obtain fH in the AC conductivity plot. For any material at a given temperature, fH can be calculated using power law40 as follows:
fH = (σdc/A)1/n
Hopping frequency fH also shows its dependency on temperature and follows the Arrhenius relation, given as follows:41
fH = fo[thin space (1/6-em)]exp (−EH/kbT)
where fo is the pre-exponential factor for hopping frequency and EH the activation energy for hopping. Furthermore, the conducting axis of the master curve is scaled by σdc. Fig. 4(E) shows the scaled AC conductivity master curve plotted between σac/σdc and f/fH. The master curve shows conductivity dispersion of the matrix. It is observed that all conductivity curves overlapped into a single curve. This indicates that the relaxation process is temperature independent under conductivity formalism.

The study of dielectric relaxation is helpful to understand the transport behaviour, the polarization effect in the polymeric film/matrix and the matrix relaxation phenomenon, which is responsible for a different kind of hopping of ions with respect to temperature. The dielectric loss tangent (tan[thin space (1/6-em)]δ) can be calculated using the following relation:

tan[thin space (1/6-em)]δ = 1/2πfRC
where δ is the dielectric loss angle, C the capacitance, R the resistance and f the frequency. tan[thin space (1/6-em)]δ also has relation with real and imaginary parts of the complex dielectric permittivity (ε*), which is given as ε[thin space (1/6-em)]tan[thin space (1/6-em)]δ = ε′′. Here ε′ and ε′′ are real and imaginary parts of the complex dielectric permittivity (ε*) respectively. This relation is also useful to calculate the tan[thin space (1/6-em)]δ value by applying the following relation:
tan[thin space (1/6-em)]δ = ε′′/ε
Fig. 4(D) shows that for a particular temperature, the tan[thin space (1/6-em)]δ value increases up to a certain limit followed by a sharp decrement with the increase in frequency due to the enhancement in polymer chain flexibility. The highest value of tan[thin space (1/6-em)]δ shows a dielectric relaxation band. The dielectric relaxation frequency (fr = 1/2πτ) observed in a tan[thin space (1/6-em)]δ spectrum is associated with polymer chain relaxation/matrix relaxation. This fr accredited electrical phenomena due to diverse components in the sample. Here τ stands for the chain/matrix relaxation time/Maxwell relaxation time, which is a parameter that depends on the intrinsic properties of the materials. The higher value of tan[thin space (1/6-em)]δ and enhancement in the value of dielectric relaxation frequency (fr) arises due to enhanced chain/matrix flexibility, where the matrix shows its optimum ionic conductivity. The poor value of tan[thin space (1/6-em)]δ and low value of fr in low-temperature regions (<40 °C) observed due to the gathering of free charge carriers near the electrode–electrolyte interface are responsible for caged-type hoping (n > 1). It is also clearly observed that the value of fr increases with the increase in temperature. This denotes the increment in the flexibility of the SPP-PEG hydrogel film, which allows ion hoping to transform from caged-type hoping (n > 1) to correlated-type hoping (n < 1) in the high-temperature region (>40 °C). Scaling of tan[thin space (1/6-em)]δ was also performed to understand more about the relaxation time variation with the change in the applied electric field and temperature. This phenomenon can be described by Kohlrauch Williams–Watt's law,42 which is given as follows:
f(t) = exp(−t/τ)β
where β is the Kohlrauch exponent (β = 1.44/FWHM).43 For a typical Debye-type relaxation behaviour, a considerable value of β and full width at half maximum (FWHM) for the typical Debye band are 1 and 1.44 respectively. The frequency axis was scaled by fmax, which is the relaxation frequency (fr). The loss tangent (tan[thin space (1/6-em)]δ) axis was scaled by the highest value of tan[thin space (1/6-em)]δ (tan[thin space (1/6-em)]δmax). The scaled plot of the loss tangent for different temperatures is given in Fig. 4(F), which clearly shows that all spectra for different temperatures completely collapsed into a single master curve. This indicates that the relaxation process is time independent under conductivity formalism. The Kohlrauch exponent (β) for the master curve is calculated to be 0.19. The value of β indicates that the hydrogel system does not obey Debye-type relaxation mechanism.

It is possible to calculate the bulk capacitance (Cb)/geometrical capacitance of the materials with Rb and fr of the sample film. Bulk capacitance (Cb) of the SPP-PEG hydrogel can be calculated using the following relation:

Cb = 1/2πfrRb
The Cb value of the material shows the charge storage capacity of the material, which also depends on the dielectric constant (ε′) and dielectric loss (ε′′) in the presence of the electric field. The charge storage near the electrode–electrolyte interface and energy loss due to the association of charge carriers in the presence of electrical field for material films are associated with the dielectric constant (ε′) and dielectric loss (ε′′) respectively. The complex dielectric permittivity (ε*) is expressed as follows:
ε* = ε′ − ′′
where ε′ and ε′′ are the real and imaginary parts of the dielectric permittivity respectively. The bulk permittivity (εb) can be calculated from the bulk capacitance using the following relation:
εb = Cb[thin space (1/6-em)]l/εoA
where Cb is the capacitance of the sample and εo the permittivity of free space. The values of Cb and εb at different temperatures for the SPP-PEG hydrogel film are given in Table S1 (ESI). The dielectric constant (ε′) and dielectric loss (ε′′) can be calculated using the following relations:
ε′ = Cl/εoA

ε′′= ε[thin space (1/6-em)]tan[thin space (1/6-em)]δ
The higher value of ε′ and ε′′ indicates the formation of space charge at the electrode–electrolyte interface, which is also known as the electrode polarization effect observed in the short-frequency region (Fig. 5A and B). Dielectric loss ε′′ is associated with the conductivity of the hydrogel film and it appears due to conductivity loss. The electrode polarization effect is suppressed for the hydrogel system at a longer frequency, as a result of the decrease in the fast periodic reversal of the electric field, and gets saturated when the frequency tends towards infinity. The relaxation bands for the matrix are observed in Fig. 5(B), and it is found that the relaxation band shifts towards higher frequencies with the increase in temperature of the sample film due to change in the phase of the matrix. The temperature-dependent dielectric permittivity study confirmed that there is an increase in electrode polarization, capacitance and loss of energy by displacement of charge with the increase in temperature.

image file: d1qm00537e-f5.tif
Fig. 5 (A and B) ε′ and ε′′ vs. f (Hz) curves plot and (C and D) Electric modulus M′ and M′′ vs. f (Hz) curve plot for the SPP-PEG hydrogel film at different temperatures, showing change in Vd, μ and D with respect to temperature.

The electric modulus is given as (M* = M′ + jM′′), where M′ and M′′ are real part and imaginary part of the complex modulus M* respectively, which is related to the complex dielectric permittivity by the following relation:

M* = 1/ε*
M′ and M′′ were calculated as follows:
M′ = ε′/(ε2 + ε′′2)

M′′= ε′′/(ε2 + ε′′2)
The electric modulus M′ and M′′ clearly shows that the large capacitance allied with the polymer in the lower frequency region, resulting in a constant line in the graph that tends to zero (Fig. 5C and D). In the lower frequency region, the value of M′ and M′′ is very poor (M =1/ε), which confirms that the electrode effect contribution is negligible, relaxation is thermally activated and charge hopping takes place.

The bulk ionic conductivity of any electrolyte also depends on the number of charge carriers, their mobility and the diffusivity constant of the matrix. The dependency of σdc on these parameters can be expressed as σdc= Nμq, where q is the elementary charge. Diffusivity constant can be calculated using the following relation:44

D = 2fmaxl2/32 (tan[thin space (1/6-em)]δmax)3
The total density of charge carriers also depends on the diffusivity constant, shown by the following relation:44
N = (σdckbT)/Dq2
The mobility of ions inside the matrix depends on the total density of charge carriers, which can be determined using the following relation:44
μ = σdc/Nq
Here the value of applied electric field (E) has to be uniform over the matrix, i.e. 250 V m−1. The drift velocity (Vd) of ions under the applied electric field can be calculated as follows:
Vd = μE
The values of D, N, μ and Vd were calculated for 20 °C, which are 3.265 × 10−9 m2 s−1, 1.03 × 1024 m−3, 3.21 × 10−5 m2 V−1 s−1 and 3.21 × 10−5 m s−1 respectively. The values of D, μ and Vd, for different temperatures are given in Table S1 (ESI), and the corresponding plot is given in Fig. 5. It is clearly observed that the value of all the three parameters increases with the increase in temperature, which is responsible for the increment in σdc.


A blend of polymeric hydrogels (SPP-PEG hydrogel) has been successfully prepared using a sodium salt inorganic polymer and a viscous organic polymer. The formation of the blend of polymers has been confirmed by infrared spectroscopy. The SPP-PEG hydrogel has a floating sandwiched matrix with good thermal stability, and has amorphous nature. The material shows good stability with a broad range of ESW potential of 2.75 V for electrochemical applications. The ionic transference number study confirms that the >96% conduction is ionic in nature. Impedance spectroscopy confirms the semiconducting behaviour of the material with a conductivity order of ∼10−4 S cm−1 at room temperature. Study of the temperature-dependent conductivity shows that the conduction mechanism follows the Arrhenius type of behaviour and the activation energy for ion movement is 0.488 eV. The study of loss tangent confirms that the matrix relaxation occurs at a low frequency with a low value, and that the relaxation frequency increases with the increase in temperature. The dielectric study clearly shows that high amount of capacitance is associated with the hydrogel material, and the modulus study confirmed that electrode effect is negligible. A well-scaled AC conductivity and loss tangent plot shows that the conductivity mechanism is time-temperature independent. The diffusivity constant and the ionic mobility increase with the increase in temperature. Since the hydrogel shows better properties in terms of thermal stability, flexibility, conductivity and dielectrics of the material ensured that the SPP-PEG hydrogel is a promising electrolyte material for energy storage devices.

Conflicts of interest

Authors declare no conflicts of interest.


Rudramani Tiwari is grateful to the Council of Scientific and Industrial Research (09/013(0874)/2019-EMR-I), New Delhi, India. Devendra Kumar is grateful to DST INSPIRE for financial support (DST/INSPIRE Fellowship/2018/IF180694). Dipendra Kumar Verma is thankful to UGC for financial support. We are thankful to Dr A. L. Saroj, Department of Physics, BHU for his guideline for electrochemical analysis. All the authors are grateful to SERB, DST (EEQ/2016/000249) for the financial support.


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Electronic supplementary information (ESI) available: Materials, methods of characterization, sample preparation, Table S1 and complete EDS report. See DOI: 10.1039/d1qm00537e

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